Milenko B. Jovanovic
The counter rotating vortex pair is depicted in the background of the cover. On the front-cover, the instantaneous visualisation and effectiveness field, measured with the imperfection located at the hole exit at the velocity ratio of 1.00, are shown. On the back-cover, mean streamlines and vorticity of the counter rotating vortex pair, measured with the perfect hole at the velocity ratio of 1.00, are presented at different streamwise positions.
The cover is designed by Milenko B. Jovanovic and Brankica Ladjevac
Film Cooling Through Imperfect Holes
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de
Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor
Promoties in het openbaar te verdedigen op donderdag 5 oktober 2006 om 16.00 uur
door
prof.dr.ir. A.A. van Steenhoven
Copromotor: dr.ir. H.C. de Lange
A catalogue record is available from the Library Eindhoven University of Technology ISBN-10: 90-386-2888-9 ISBN-13: 978-90-386-2888-2
This research was financially supported by the Dutch Technology Foundation STW (project EWO.5478)
Παντα %ει και oυδεν µενει Everything flows, everything changes
(Heraclitus)
To my parents Marija and Bogdan for all their love and time dedicated to me
vi
Contents
1 Introduction 1 1.1 Historical overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Why cooling in gas turbines? . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Film cooling and previous research . . . . . . . . . . . . . . . . . . . . 4 1.4 Jet in cross-flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Scope and outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Experimental Set-Up 11 2.1 Water channel set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Laser induced fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Particle image velocimetry . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 Flow fields and identification of vortices . . . . . . . . . . . . . . . . . 15 2.5 Liquid crystal thermography . . . . . . . . . . . . . . . . . . . . . . . . 22 2.6 Perfect and imperfect holes . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Flow Field Characteristics 31 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Jet and cross-flow properties . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 Cross-flow boundary layer on flat plate . . . . . . . . . . . . . . 32 3.2.2 Main characteristics of submerged jet . . . . . . . . . . . . . . 33
3.3 Jet cross-flow interaction along central plane . . . . . . . . . . . . . . 35 3.3.1 Visualisations and central plane borders . . . . . . . . . . . . . 35 3.3.2 Velocities and vortical structures along the central plane . . . . 39 3.3.3 Distribution of vortical structures and their vorticity . . . . . . 49
3.4 Horizontal measurements above the hole . . . . . . . . . . . . . . . . . 52 3.4.1 Perfect hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.4.2 Imperfect hole with inner-torus 2 . . . . . . . . . . . . . . . . 55
3.5 Lateral measurements and counter rotating vortex pair . . . . . . . . . 56 3.5.1 Spanwise flow fields . . . . . . . . . . . . . . . . . . . . . . . . 56 3.5.2 Average values of counter rotating vortex pair . . . . . . . . . . 59
3.6 Analysis and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.6.1 Windward and lee vortices . . . . . . . . . . . . . . . . . . . . 63 3.6.2 Spiral vortices . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.6.3 Counter rotating vortex pair . . . . . . . . . . . . . . . . . . . 65
viii REFERENCES
3.6.4 Flow field and its three-dimensional representation . . . . . . . 66
4 Adiabatic Film Cooling Effectiveness 67 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2 Perfect hole and effectiveness representation . . . . . . . . . . . . . . . 68
4.2.1 Two-dimensional plots . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.2 Equivalent cooled width . . . . . . . . . . . . . . . . . . . . . . 70 4.2.3 Equivalent cooled length . . . . . . . . . . . . . . . . . . . . . . 71 4.2.4 Equivalent cooled surface . . . . . . . . . . . . . . . . . . . . . 72
4.3 Imperfection position and turbulence intensity . . . . . . . . . . . . . 73 4.3.1 Two-dimensional plots . . . . . . . . . . . . . . . . . . . . . . . 73 4.3.2 Equivalent cooled length . . . . . . . . . . . . . . . . . . . . . . 78 4.3.3 Equivalent cooled width . . . . . . . . . . . . . . . . . . . . . . 79 4.3.4 Equivalent cooled surface . . . . . . . . . . . . . . . . . . . . . 80
4.4 Imperfection and asymmetry . . . . . . . . . . . . . . . . . . . . . . . 82 4.4.1 Two-dimensional plots . . . . . . . . . . . . . . . . . . . . . . . 82 4.4.2 Equivalent cooled width . . . . . . . . . . . . . . . . . . . . . . 84 4.4.3 Equivalent cooled surface . . . . . . . . . . . . . . . . . . . . . 85
4.5 Size and shape of imperfection . . . . . . . . . . . . . . . . . . . . . . 86 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5 Heat Transfer Measurements in Compressible Flow 89 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2 Ludwieg tube set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.1 Ludwieg tube and its principle . . . . . . . . . . . . . . . . . . 90 5.2.2 Measurement techniques . . . . . . . . . . . . . . . . . . . . . . 92 5.2.3 Jet set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.2.4 Heat transfer of film cooling in compressible flow . . . . . . . . 97
5.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6 Conclusions and recommendations 107
References 111
B Colors and Their Representation 121
C Submerged jet 125 C.1 Perfect hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 C.2 Imperfect holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
D Central plane measurements 131 D.1 Visualisations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 D.2 PIV data along central plane . . . . . . . . . . . . . . . . . . . . . . . 133 D.3 Counter Rotating Vortex Pair . . . . . . . . . . . . . . . . . . . . . . . 137
REFERENCES ix
D.3.1 Perfect Hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 D.3.2 Inner-torus 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 D.3.3 Inner-torus 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Summary 147
Samenvatting 149
1.1 Historical overview
A turbine is a rotary engine that extracts energy from a fluid motion. Claude Burdin coined the term from Latin turbine, which means whirl. The origin of the first turbine is probably a water wheel and it was invented in Persia or China. It was used for grinding corns into flower in the first century B.C. The first turbine was invented in the first century A.D. by Heron of Alexandria and it was named Aeolipile (Latin pila - ball and aeoli comes from Aeolus - Greek god of the wind). Aeolipile is a rotational wind ball driven with steam propulsion. It can rotate 1500 rpm and develop one tenth of a horse power (power of a man) and it has had an efficiency of only 1%. Aeolipile was just a toy and it did not have any industrial application. Around the seventh century the first windmills are developed. In pre-industrial Europe, the windmills were employed for grain-grinding, irrigation or drainage pumping using a scoop wheel, to saw logs into beams, boards and laths, in the paper production and in the processing of other commodities such as spices, cocoa, paints and tobacco. The real revolution in transport and industry, which has totally changed the world, occurred in the nineteenth century. It was brought out by the invention of a steam engine (Thomas Savery in 1698) and its application in industry. The first industrial gas turbine was constructed by J. F. Stolze and it was patented in 1899. Although its efficiency was only 4%, this gas turbine was a groundwork for many other gas turbines.
Nowadays, turbines are among the most powerful machines ever made. They are used for aircraft and ship propulsion, to power trains, ships and tanks but also in elec- tricity generation and industrial applications. The simplest gas turbine consists of an upstream compressor coupled with a downstream turbine and a combustion chamber in-between them (see fig. 1.2a). Energy is added to the gas stream in the combustor, where air is mixed with fuel and ignited. Combustion increases the temperature, ve- locity and volume of the gas, which continues to flow over the turbine blades, spinning the turbine and powering the compressor. Gas turbines for electrical power produc- tion are particularly efficient. The efficiency is larger than 40% and it can reach 60% if wasted heat from the gas turbine is recovered by a conventional steam turbine in a combined cycle configuration. A gas turbine used for flying is the most interesting and demanding machine. A jet engine is any engine that accelerates and discharges a fast moving jet of fluid to generate thrust in accordance with Newton’s third law of motion. Its main component is a gas turbine, which is used for generating a jet of high speed exhaust gases for propulsive purposes. In England on the 16th of January 1930, Frank Whittle submitted patents for a full-scale aircraft engine. Independently, Hans von Ohain started work on a similar design in Germany in 1935. Ohain and Ernst
2 Introduction
Heinkel crafted the first jet plane. The experimental Heinkel He 178 flew on the 27th of August 1939. The engine applied to drive this aeroplane produces a thrust of 3.7 kN . Today, gas turbines rotate with more than 10, 000 rpm and jet engines produce a thrust of 410 kN (see fig.1.1).
Figure 1.1. The jet engine Trent 1000 is a turbofan produced for Boeing’s aircraft 787. It produces a thrust of 333kN and it consists of a fan, 8 stages of low pressure and 6 stages of high pressure compressors. After a combustion chamber the gas flows into a turbine, which has 1 high pressure stage, 1 intermediate pressure stage and 6 low pressure stages. [This photograph is reproduced with the permission of Rolls-Royce, copyright c©Rolls-Royce plc 2005].
1.2 Why cooling in gas turbines?
Ideal gas turbines are thermodynamically described with the Joule-Brayton cycle (see fig. 1.2b). In the ideal cycle, compression and expansion of a gas are adiabatic and isentropic. The change of kinetic energy is negligible. There are no pressure losses in the combustion chamber and exhausting ducts. The working fluid is a perfect gas which properties are constant.
For this ideal cycle the efficiency and net work can be calculated as a function of the pressure ratio and temperature ratio. From the first law of thermodynamics we get:
qAB = (hB − hA) + 1 2 (v2
B − v2 A) + w (1.1)
where q and w are the exchanged heat and work per unit mass among points A and B. The enthalpy is denoted with h and velocity with v in points A and B. The cycle efficiency e and specific work output, for the Joule cycle, can be calculated as (for more see Cohen et al. [8]):
e = q23 + q41
w
γ−1 γ
r − 1) (1.3)
where pr = p2/p1 = p3/p4 is the pressure ratio, tr = T3/T1 is the temperature ratio, γ is the specific heat ratio and cp is specific heat at constant pressure. The efficiency of the Joule cycle depends only on the pressure ratio and type of the gas. The specific work, which is an important parameter for a jet engine, is a function of the temperature and pressure ratio (for more see Cohen et al. [8]). From equation 1.3, taking into account that T1 ≈ constant, it follows that a larger turbine inlet tempera- ture (T3) means greater work and efficiency, which is in agreement with experiments. In state-of-the-art gas turbines the turbine inlet temperature exceeds 2000K. This temperature is higher than the melting point of materials used to produce gas tur- bines. Therefore, turbine blades, vanes and elements of a combustion chamber must be cooled. The coolant is air extracted from the compressor of the jet engine. Since this extraction decreases the thermal efficiency, it is necessary to understand and optimise the cooling technique, operating conditions and a turbine blade geometry.
(a)
s
T
1
(b)
Figure 1.2. a) A schematic drawing of the simplest gas turbine and b) the Joule- Brayton cycle.
Gas turbine blades are cooled internally and externally. Internal cooling is achieved with the coolant, which passes through several enhanced serpentine passages inside blades and extracts the heat from their surface. Both jet impingement and pin-fin cooling are also used as a method of internal cooling. External cooling is also called film cooling. Internal coolant air is ejected through discrete holes (see fig. 1.3a) or slots to provide a coolant film, which protects the outside surface of a blade from hot combustion gasses. The advantage of this technique is the avoidance of direct contact between turbine blades and hot gases.
Film cooling holes in turbine blades have been produced by means of electro discharge, electro chemical and laser drilling. In the last few years the application of laser drilling has increased. The laser drilling process is fast but also crude. Higher laser intensities may lead to a cruder nozzle shape, which in turn most certainly has an effect on the flow (Kohli and Thole [43]). During laser drilling the material is melted and ejected from the drilled hole. If the melted material, produced by means of laser drilling, stays inside the hole it resolidifies and forms a production imperfection
4 Introduction
(fig. 1.3b and 1.3c). The production imperfection may reach 25% of the hole diameter. Therefore, a detailed study is needed to investigate the influence of the production imperfection on film cooling.
(a) (b)
(c)
Figure 1.3. a) A turbine blade with film cooling holes. b) The side view of a laser drilled hole with imperfections and c) the top view of a resolidified melt-ejection inside the film cooling hole.
1.3 Film cooling and previous research
A film cooling process depends on many parameters. Primary physical properties, that influence film cooling, are: a coolant-to-hot mainstream velocity ratio, blowing ratio, momentum ratio, pressure ratio, temperature ratio, density ratio and turbulence intensity. Also, the geometrical characteristics have a bearing on film cooling. There- fore, a geometry of an airfoil and film cooling holes, their distribution and location have been widely studied. In a typical gas turbine airflow, the pressure ratio varies from 1.02 to 1.10, while the corresponding blowing ratio takes values approximately from 0.5 to 2.0. The temperature ratio is within 0.5 − 0.85 and the corresponding density ratio varies approximately from 2.0 to 1.5 (Han et al. [25]).
Film cooling has been studied on a real or simplified geometry, using only one or multiple holes. The experiments on a real gas turbine are demanding and it is very difficult to obtain results under real engine conditions. Due to this reason, there are few results on real rotating blades. Dring et al. [9] were among the first to measure a film cooling effectiveness on the rotating blade. A large number of other studies have been conducted under easier working conditions and/or on simplified geometries.
1.3 Film cooling and previous research 5
Drost and Bolcs [10] investigated the heat transfer on a static film cooled gas turbine airfoil. They found that an enhanced blowing ratio (see equation 2.1) decreases cooling on the suction side of the airfoil for a single row of film cooling holes and improves cooling for the staggered hole arrangement. The higher film cooling effectiveness is detected in the near hole region with an approaching laminar boundary layer. A dense coolant increases the effectiveness and heat transfer on the suction side. On the pressure side the heat transfer is reduced. The free stream turbulence intensity weakly affects cooling on the suction side. On the pressure side the effectiveness is increased at larger turbulence levels and heat transfer ratios are lower.
Early studies have proved that the results obtained on simple flat-surface models can be applied to real engine design with slight corrections (Han et al. [25]). A flat plate model is relatively simple and less expensive. Therefore, many researchers have used this model to study film cooling.
Ammari et al. [1] presented the effect of density ratio on heat transfer coefficients. They showed that experiments performed with a density ratio of unity must be scaled. Spanwise average heat transfer coefficients obtained at different density ratios corre- spond well to the function (x/d)(uj/u∞)−4/3 proposed by Forth and Jones [12] (here x is a distance from the hole with the diameter d; uj and u∞ are velocities of the jet and cross-flow respectively).
Sinha et al. [62] investigated the influence of density ratio on the film cooling effec- tiveness. They found that a decrease in density ratio and an increase in momentum ratio reduce the lateral average effectiveness. The effect of density ratio on the flow field was studied by Pietrzyk et al. [55]. They found that a change in density ratio does not influence flow patterns but it can not be simply scaled either with a blowing ratio or momentum ratio.
Goldstein and Yoshida [17] examined the influence of a laminar/turbulent bound- ary layer of the cross-flow on a laminar/turbulent jet injected through cylindrical inclined holes. Their measurements show that the turbulent jet gives a better cool- ing effectiveness compared to the laminar at the same blowing ratio. Hay et al. [28] reported that the approaching boundary layer does not have any influence on cooling under the film. Rutledge et al. [56] investigated the influence of surface roughness on the heat transfer. Upstream roughness enlarges the boundary layer thickness three times. The mixing is increased and the heat transfer coefficient is two times larger than on the smooth blade. But the benefit of the film cooling relatively increases compared to the uncooled case.
The impact of free stream turbulence on film cooling was studied by Mayhew et al. [48]. They measured the adiabatic film cooling effectiveness by means of liquid crystal thermography. It has been reported that the influence of free stream turbulence has an effect on cooling but it is not so significant and this influence can be neglected at higher blowing ratios.
An important parameter is a discharge coefficient. It represents the ratio of a real mass flow to the ideal mass flow and it was studied by Hay and Spencer [29] and Gritsch et al. [22]. Besides the flow parameters Goldstein and Eckert [16] investigated the influence of hole geometry on film cooling. For a mass blowing ratio lower than 0.5, a cylindrical hole has a comparable effectiveness as a shaped hole which exit cross section is widened for about 10 degrees. At higher blowing ratios, the shaped hole
6 Introduction
produces much better effectiveness. That the geometry of holes affects film cooling has also been shown by Gritsch et al. [21]. They compared heat transfer coefficients produced by means of cylindrical, fanshaped and laidback fanshaped film cooling holes. Their influence on the flow field was examined by Thole et al. [65]. The effect of the compound angle film cooling holes on heat transfer coefficients was studied by Sen et al. [61]. A complementary investigation, conducted by Schmidt et al. [59], reports the effect of the compound angle on the adiabatic effectiveness. Cho et al. [7] examined the hole orientation and its influence on film cooling. They stated that holes with a lateral injection angle produce better cooling than streamwise oriented holes.
Not only the shape but also an inclination of the hole can modify film cooling performances. Yuen and Martinez-Botas [70] measured the adiabatic effectiveness by means of liquid crystal thermography. They investigated the influence of the blowing ratio and streamwise angle on the effectiveness. Three angles (30o, 60o and 90o) have been tested. The angle of 30o shows the best cooling characteristics. It has been reported that the more effective region, in which the effectiveness is larger or equal to 0.2, is not found beyond 13 diameters from the hole trailing edge. Yuen and Martinez-Botas [69] investigated also the impact on the heat transfer coefficient. An investigation of inner hole geometry can be found in Hale et al. [24]. They investigated the influence of a plenum on film cooling and found that the plenum geometry has an effect on the film cooling effectiveness, which depends on the injection hole length and streamwise hole angle.
The effect of the hole length in the film cooling process was demonstrated in the study of Lutum and Johnson [47]. It has been reported that the length to diameter ratio larger than 7, has a small effect on the film cooling effectiveness. However, for shorter holes a decline in the hole length to diameter ratio decreases the film cooling effectiveness and the lowest value is detected for the shortest hole. As far as the author is aware there is no open study, which examine the imperfection influence on film cooling.
1.4 Jet in cross-flow
Figure 1.4. A two-dimensional sketch of the jet cross-flow interaction with film cooling characteristics. u∞ is the free stream velocity, the jet velocity is denoted as uj . Tw and Tf are the wall and film temperatures respectively.
1.4 Jet in cross-flow 7
In this thesis the influence of a discrete hole imperfection on film cooling is ex- amined experimentally. To localise effects and reduce the number of variables the geometry of a blade is simplified. Since the hole diameter d is much smaller than the radius of the blade a flat surface model has been used. This model can be applied to real engine design with slight corrections. Film cooling over the flat plate is created by means of a jet injected into a cross-flow boundary layer through only one hole (see fig. 1.4). This model is known in the literature as a jet cross-flow interaction. Besides film cooling, a jet in cross-flow is relevant to many other engineering applications such as fuel injection, smokestack pollution dispersion, V/STOL (vertical short take off and landing) aircraft control etc. Although similar characteristics can be found in all these flow fields, details can be quite different depending on many variables. A blowing ratio (see equation 2.1) can be used for distinguishing flows. When the blowing ratio is lower than 2, it can be said that a jet in cross-flow represents a film cooling process.
The jet in cross-flow has been widely investigated. One of the first detailed inves- tigations of the jet in cross-flow has been reported by Bergeles et al. [5]. They found that the blowing ratio is a very important parameter in the film cooling process. They detected the maximal velocity of the jet in the vicinity of the hole trailing edge and found that three quarters of the jet mass flow come out of the ‘lee half’ of the hole.
A blade cavity, from which air is injected into holes, is simulated with a plenum. Peterson and Plesniak [53] examined the influence of the supply plenum on short hole film cooling. They detected that the plenum feed direction strongly influences the flow field and therefore the heat transfer. Johnston et al. [35] showed that the inlet geometry significantly changes the near flow field and does not have a large influence on the far field. The influence of the hole geometry was investigated by New et al. [51]. They conducted experiments with different elliptical holes. Andreopoulos [2] has found that the cross-flow penetrates the jet hole up to three diameters at low blowing ratios. Turbulence characteristics of an isolated normal jet in a cross-flow have been examined by Andreopoulos and Rodi [3]. They detected a vortex motion in the ‘wake’, and the shear layer above it.
Fric and Roshko [13] studied experimentally vortical structures in the wake of the transverse jet at larger velocity ratios. They classified vortical structures into a shear layer, horseshoe and wake vortices and a counter rotating vortex pair. Kelso et al. [40] investigated experimentally the genesis and development of vortical structures in the jet cross-flow interaction. Morton and Ibbetson [49] analysed the warp mechanism of the vortical structures. Haven and Kurosaka [26] examined an impact of the hole geometry on the development of flow structures. They showed that the hole geometry influences the development of flow structures. By manipulating the hole geometry, the lift-off of the jet as well as the cross-flow entrainment can be regulated.
A number of flow structures have been identified in the interaction region of the jet and cross-flow. The occurrence of these structures depends on local details of the geometry and flow conditions. Moussa et al. [50] studied the mixing of the jet in a cross-flow. Smith and Mungal [63] investigated mixing, structures and scaling. A jet in a cross-flow have been studied numerically, too (see Yuan et al. [68]). In my article Jovanovic et al. [39], we analysed the effect of a discrete imperfection inside the short perpendicular hole. An additional vortex is detected in the imperfect case. It has
8 Introduction
(a) (b)
Figure 1.5. a) Vortical structures generated by means of jet cross-flow interaction with film cooling characteristics. b) The hole exit, nomenclature and the coordinate- system.
also been concluded that this vortex changes the film cooling effectiveness. From the literature survey, it can be concluded that multiple vortical structures
are produced in case of the jet cross-flow interaction. They are a function of ratios of jet and cross-flow parameters: the velocity ratio (V R), the blowing ratio (BR) and the momentum ratio (MR) (they are defined in section 2.1). A typical blowing ratio applied in film cooling is lower than 2. Even at low BR-s the jet cross-flow interaction generates a turbulent flow, which is dominated by coherent motion. Four large vortical structures have been detected in this turbulent flow (see fig. 1.5): a counter rotating vortex pair (CVP), horseshoe vortex (HSV), windward (WV) and lee vortex (LV). CVP is the largest vortical structure, which occurs in the jet cross- flow interaction. The main vorticity of these structure originates from the side rims of a hole. Vortices roll up at the hole rims and due to the shear between the jet and cross-flow they continue to warp and manifest downstream (see Haven and Kurosaka [26]). The horseshoe is the smallest structure with a negligible effect on film cooling. It forms in a similar way as in the flow around a blunt body. The pressure difference, which arises at the jet boundary, drives a vortex roll. This roll-up is the origin of a horseshoe vortex. Around a jet injected into a steady surrounding a toroidal separation vortex is formed. If the jet is exposed to a cross-flow the torodial vortex breaks and the windward and lee vortices are formed (for more see Lim et al. [44]). The injected jet separates over the surface, and downstream of the hole it rolls and breaks to turbulence. The region downstream of the film cooling hole will be named here the cooling volume. The boundary between the flat plate and cooling volume is called here the cooled surface.
Film cooling depends strongly on thermodynamical parameters. If the tempera- ture of the free stream is T∞ and of the wall is Tw then the heat flux without film cooling can be calculated as:
q′′0 = h0(T∞ − Tw) (1.4)
1.5 Scope and outline 9
where h0 is the heat transfer coefficient on the plate surface. When the jet is injected into a cross-flow a film is formed on the surface with the temperature Tf and the heat transfer coefficient changes from h0 to h. Then, the heat flux becomes different and can be calculated as:
q′′ = h(Tf − Tw) (1.5)
In the case of a compressible flow, the recovery temperatures of T∞ and Tf must be used (for more see chapter 5).
To obtain any benefit from film cooling the heat transfer should be lower than in the case when cooling is absent. Therefore, the ratio q′′/q′′0 should be lower than 1.0:
q′′
θ = T∞ − Tj
T∞ − Tw (1.7)
η = T∞ − Tf
T∞ − Tj (1.8)
and η is called a film cooling effectiveness. To calculate the heat transfer on a blade or vane the heat transfer coefficient and film cooling effectiveness must be known.
1.5 Scope and outline
The aim of this work is to measure the effectiveness and heat transfer with a perfect hole and to examine the influence of the production imperfection on them. Besides quantifying effects of an imperfection on thermodynamical properties I also want to know the answer on the question why an imperfection has any influence and what is the influence of various dimensionless parameters (like the velocity ratio and Mach number). To this end I conducted experiments in a water channel and heat transfer measurements in a Ludwieg tube. This work is realised as the part of STW project EWO.5478.
In chapter 2 the experimental methods used in the water channel measurements are described. The set-up is scaled in such a way that the Reynolds number is similar to the one detected in a gas turbine. Particle image velocimetry is applied to conduct the velocity measurements. The vortex detection algorithm is explained and measurement uncertainties are given. The flat plate is made from plexiglas. Since plexiglas is a bad heat conductor the plate wall is treated as adiabatic. By measuring the wall temperature the film cooling effectiveness can be calculated by using equation 1.8. The temperature on the wall is measured with thermochromic liquid crystals.
In chapter 3 attention is given to the genesis of large vortical structures in the case of the perfect hole and in the cases of two idealised production imperfections. The emphasis is put on the formation of vortical structures, their merging, transport and
10 Introduction
influence on the flow field. Average flow fields are presented and analysed. Although average values are very important, to understand the physics and behaviour of vortical structures, instantaneous flow fields must be also studied (see Lourenco et al. [45]). Therefore, instantaneous data with the vortical structure behavior are discussed in the second part of this chapter.
The adiabatic film cooling effectiveness is studied in chapter 4. The experiments have been conducted at different velocity ratios with diverse imperfections. Two free stream turbulent intensities have been investigated. The position of a discrete imperfection is varied. Three half-toruses are placed simultaneously inside the hole to simulate a multiple imperfection. Symmetrical and asymmetrical imperfections are compared and the magnitude of the torus blockage is also varied. Results of these measurements are presented and studied in chapter 4.
To investigate compressibility effects on film cooling a Ludwieg tube (called also expansion tunnel) has been employed. The Mach and Reynolds numbers can be adjusted independently. The set-up is rescaled similar to the one, which is used in the water channel. In the first part of chapter 5 the experimental set up, measurement technique and uncertainties are explained. The heat flux is measured by means of thin film gauges. From the heat flux, the film cooling effectiveness and heat transfer coefficient are extracted. The results obtained in the expansion tube are compared to the results from the water channel.
The conclusions of this work together with future recommendations are given in chapter 6.
Chapter 2
Experimental Set-Up
2.1 Water channel set-up
Part of experiments were performed in a closed-return water channel shown in fig. 2.1 at the Technische Universiteit Eindhoven (Eindhoven University of Technology). The optically accessible volume of the test section is the volume of a cuboid with dimen- sions 2000 x 550 x400 mm. To obtain a water flow with a uniform velocity, a pair of flow straighteners was placed at the inlet of the test section. The flow straighteners consist of rectangular combs (with a characteristic rectangle 6.1 x 5.2 mm) and a metal mesh (with a characteristic dimension 1.5 mm). This combination provides a uniform flow with a turbulent intensity of 2% in the test section. By placing a static grid, with the mesh size of 40mm and the rod diameter of 8mm, in the vicinity of the flow straightener, a turbulence intensity of approximately 7% has been measured 620mm downstream from the grid. The speed inside the test section can be varied from zero till 0.20 m/s. During experiments a flat plate (2400 x 565 mm) made of plexiglas had
Figure 2.1. The water channel.
been placed in the test section. The leading edge of the flat plate was located 300 mm from the nearest flow straightener. Below the leading edge an array of suction holes was made on the bottom of the test section to prevent (reduce) boundary layer separa- tion. The jet is injected through a cylindrical hole into the cross-flow boundary layer. The jet set-up is independent of the water channel and consists of a vessel, pump, flow meter, plenum and pipe (see fig 2.2). The vessel of 0.45 m3 in volume is used for adjusting the jet conditions (volume flow, temperature or dye concentration). Water from the vessel is pumped into the plenum, which simulates a cavity inside blades. The jet volume flow is measured and controlled by means of a flow meter with an error of 2%. At the plenum outlet a small flow straightener is implemented to suppress the formation of large turbulent structures. The pipe, which connects the plenum and test section, is inclined and the angle is 37o.
The scaling of the set-up is based on the corresponding Reynolds numbers and
12 Experimental Set-Up
Figure 2.2. The jet set-up. Numbers depict: 1 - vessel, 2 - pump, 3 - by-pass, 4 - volume flow-meter and 5 - plenum.
the boundary layer thickness of the cross-flow. The leading edge of the hole is located 1.625 m from the plate leading edge. With the speed of 0.20 m/s, which is used in the water channel experiments, the Reynolds number based on the length is Rexl = u∞ xl
ν = 3.23 x 105 (ν is the kinematic viscosity, xl is the distance of the leading edge of the hole from the plate leading edge). This corresponds to a real situation in a gas turbine. The diameter of the hole is set to d = 57 mm. By changing the jet volume flow the ratio between the average jet velocity and free stream velocity is varied from 0.15 to 1.50. Hence, the jet Reynolds number, based on the average jet velocity and diameter of the hole d, Red = ujd
ν is between 1.70 x 103 and 1.70 x 104. The film cooling holes are inclined. The inclination between the axis of the hole and blade surface is usually from 30o to 40o. In our experiments the inclination of the hole is 37o. The hole length (l) to diameter (d) ratio is 10.
Important normalised kinematic parameters that describe film cooling are: a blowing ratio BR, velocity ratio V R and momentum ratio MR and they are defined here.
The blowing ratio is defined as:
BR = ρjuj
ρ∞u∞ (2.1)
where uj and u∞ are the surface average velocities of jet and the free stream velocity while ρj and ρ∞ are the jet and free stream density respectively.
The velocity ratio is defined as:
V R = uj
u∞ (2.2)
and it is equal to the blowing ratio for the unity density ratio. The momentum ratio:
MR = ρju
2 j
2.2 Laser induced fluorescence 13
is a product of the blowing and velocity ratio if the jet profile has the same sign over the whole outlet surface.
In the water channel BR = V R and MR = V R2. Therefore, the jet cross-flow interaction is only characterised by V R. In a compressible flow, due to difference in densities, the interaction depends on a combination of all three parameters.
2.2 Laser induced fluorescence
Figure 2.3. The LIF visualisation performed with the perfect hole at the velocity ratio equals to 1.00.
Laser induced fluorescence (LIF) is applied to visualize the flow field and to mea- sure relative concentration. LIF is a process whereby molecules fluoresce (re-emit energy) after they have been excited to higher energy levels by absorption of elec- tromagnetic radiation (i.e. laser). The intensity of this fluorescence is, in general, a function of the species concentration and fluid temperature. Fluorescein sodium salt (C20H10Na2O5), which has been used in experiments, is only concentration sensitive. This means that by measuring the intensity of emitted light, the concentration can be determined. The fluorescence detected by means of a camera can be expressed as:
Imeas(c(−→r , t),−→r , t) = I0(−→r , t)A0(−→r )φε λe
λf c(−→r , t) + Ioff (−→r , t) (2.4)
where A0 is the fraction of the detected fluorescence light, which depends on the experimental set-up and camera. I0 is the intensity of the laser sheet (in the present case, it depends on position and time), c is the molar concentration of the fluorescein dye, ε is the absorption coefficient, λe
λf (the wavelength ratio) accounting for the energy
loss in the excited state, φ is the quantum efficiency and Ioff is the offset intensity of the camera. For fixed optical settings the normalised concentration can be expressed as:
C(−→r , t) = c(−→r , t) c(−→r0 , t)
= Imeas(c(−→r , t),−→r , t)− Ioff (−→r , t) Imeas(c(−→r0 , t),−→r0 , t)− Ioff (−→r0 , t)
(2.5)
where C is the normalised concentration, c(−→r0 , t) is the known concentration in the image at time t. Ioff is the background noise of a camera, which is determined by taking a few images when the laser is switched off.
Since the light of an Nd:Yag laser is not constant neither in space nor in time, it is assumed that the variation in light intensity is constant along rays which emanate from one point (x∗, y∗). The origin can be found by capturing a few images when the concentration of dye is constant along the whole image. To measure the
14 Experimental Set-Up
concentration in a point (xi, yi) during an experiment, the line x−xi
xi−x∗ = y−yi
yi−y∗ must across the field in the image with the known concentration.
In the experiments the channel flow was dyed by means of fluorescein sodium salt (Mr = 376.28), with the concentration c0 ≈ 10−4 mol/m3. The fluorescent light was captured with a similar camera used in PIV measurements. To filter the laser light (λ = 532nm) a high-pass filter was employed (holographic notch filter: 0% transmission at λ = 532nm and 80% at λ = 575nm). The images are stored on a computer using the acquisition software VideoSavant.
2.3 Particle image velocimetry
Optical measurement techniques are convenient for velocity quantifications and flow field visualisations. One of them is particle image velocimetry or simple PIV. Mea- suring the fluid lump displacement in known time a velocity can be determined:
−→v = ds
dt −→τ =
t −→ei (2.6)
where −→v is the fluid lump velocity, with its path s in the time t. xi is the dis- placement in a coordinate-system defined by the basis vectors −→ei . With PIV the displacement in two or three directions is simultaneously measured in a short known time interval t. A flow can be traced by using particles which are able to follow a fluid motion. If the flow is seeded and illuminated with stroboscopic light, it can be visualised and photographed. Dividing photographs into small areas, named in- terrogation windows, and applying the pattern recognition technique based on the cross-correlations on two subsequent photographs, the displacement can be deter- mined. The time interval is fixed by the frequency of stroboscopic light. The seeding determines the quality (error, reliability, spatial resolution etc.) of PIV measurements. A suitable seeding for PIV should be non-perturbing, homogeneously spread in the flow, efficient in scattering light and with a minimal velocity lag. The non-perturbing character relies on the assumption that the influence of the tracer particles on the fluid is negligible. This is valid when the diameter of particles is much smaller than a typical length scale of the flow and when the difference in densities is small enough. If this is fulfilled, it can be assumed that the motion of particles is identical to the motion of the surrounding fluid. To achieve this the water channel is seeded with neu- tral buoyant tracers. Polyamide seeding particles made out of polyamide 12 with the density ρPSP = 1.03 kg/m3 and a mean diameter of 20 µm have been employed. The sketch of the PIV set-up is given in fig. 2.4. As a light source a dual-pulse Nd:Yag laser (λ = 532 nm) is used. The laser sheet is formed by means of a negative lens and its thickness is determined with a rectangular diaphragm. Images were taken with CCD cameras (Kodak Megaplus 1008 x 1018 pixels, 10 bits = 1024 grayscales) and stored on hard disks using the acquisition software VideoSavant. The sampling frequency was f = 14.8 Hz, which is limited by the Nd:Yag laser. The PIV software, used for
2.4 Flow fields and identification of vortices 15
precessing the data, was developed at the Technische Universiteit Eindhoven. The software uses a standard algorithm to cross-correlate particle images in interrogation areas with a sub-pixel interpolation (see Bastiaans et al. [4]).
Figure 2.4. The set-up used for measuring the velocity by means of particle image velocimetry - PIV.
In the analysis I have been using interrogation windows of 32 x 32 pixels with an overlap of 50%. The time delay between two subsequent images has been set to achieve a displacement between 2 − 4 pixels. The uncertainty in the peak-finding algorithm is estimated to be 0.1 pixels, which gives an error in the velocity measurement of εpf = 4%. The average flow field and other statistical results were obtained by averaging and processing 250 or 1000 frame pairs per measurement. The estimated total error (
√ ε2
pf + ε2 r) of the velocity is between 4%−6%. It depends on the number
of samples and the turbulence intensity (details are shown in appendix A and relative errors (εr) are given in table A.2). The relative error of the turbulence intensity is 11% for 250 pairs and 6.5% for 1000 pairs with a confidence interval of 95%. Errors of normalised values are higher because of the error propagation and they are: 5%, 6.5% and 13.5% for normalised values of velocities, rms-s and turbulent kinetic energy respectively, using an ensemble of 1000 data at Tu = 0.30.
2.4 Flow fields and identification of vortices
To test and explain methods used in the PIV analysis, measurements performed with a short perpendicular hole are used. The set-up, which is different from the one described in section 2.1, and physical properties are studied in my article Jovanovic et al. [39]. In fig. 2.5 two instantaneous flow fields are depicted. The flow consists of the perpendicularly injected jet into the cross-flow, which comes from left. All values are normalised by the free-stream velocity u∞ and the hole diameter d.
In the flow field, shown in fig. 2.5a, a rotational motion is visible, while in the other flow field it is absent. But is the visualized vortical motion the only one swirl
16 Experimental Set-Up
in this flow field? To answer this question transformations must be applied to the instantaneous flow fields.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0
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Y [
] (a)
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1
X [ ]
Y [
(b)
Figure 2.5. Instantaneous flow fields and the vector representation. The jet is perpendicularly injected into the cross-flow. a) The rotational motion is visible around the coordinate (1.4, 0.3) and b) the rotational motion is not detected. The dimensions are normalised with the hole diameter d and the free-stream speed u∞. The leading edge of the hole is located at X = 0.
The common transformation is the Galilean transformation. This is nothing else but the linear transformation of velocity:
−→v g = −→v −−→v const (2.7)
where −→v is an instantaneous velocity and −→v const is a uniform (spatially constant) velocity. In fig. 2.6 the result of the Galilean transformation applied on the above de- picted velocity fields is shown. Two vortices are detected in the left figure and three
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0
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(a)
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0.2
0.4
0.6
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1
X [ ]
Y [
(b)
Figure 2.6. Instantaneous flow fields after the Galilean transformation. a) Two vortices are visualised, b) three vortices are visible. The dimensions are normalised with the hole diameter d and the free-stream speed u∞. The leading edge of the hole is located at X = 0.
in the right. The Galilean transformation is a powerful tool which can educe any kind of a vortical motion but its effect depends on −→v const. When the velocity field is strongly anisotropic, e.g. in boundary layer flow, the constant velocity used to trans- form an instantaneous flow field is mostly equal to a predominant velocity component. But in the case with a strong ‘two-dimensional’ shear layer, like in our example, the ‘constant’ velocity should be varied in time to visualise the flow nicely. Therefore, it
2.4 Flow fields and identification of vortices 17
would be very difficult to automate this method. This is a big disadvantage of the Galilean transformation.
Using the Reynolds decomposition an instantaneous flow field can be separated into its average and fluctuational parts:
−→v = −→v +−→v ′ (2.8)
where −→v is the average velocity and −→v ′ is its fluctuation part. I assume that my
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0
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(a)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0
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1
X [ ]
Y [
(b)
Figure 2.7. Fluctuation flow fields obtained using the Reynolds decomposition. a) Three vortices are visualised, b) three vortices can be seen. The dimensions are normalised with the hole diameter d and the free-stream speed u∞. The leading edge of the hole is located at X = 0.
process is ergodic. Therefore, averaging over an ensemble or in time should be the same if a sample is long enough. In fig. 2.7 the fluctuation fields are depicted. Three rotational structures are detected in the left figure and the same number in the right. Although, the major vortical structures are similar to fig. 2.6 differences are clearly visible. Two clockwise vortices are extracted by the Reynolds decompositions (see fig. 2.7 above X = 0.4) and they are not detected in fig. 2.6 using the Galilean transformation. The disadvantage of the Reynolds decomposition is that it requires the ‘large’ number of data but when this is fulfilled the visualisation can be easily automated.
The last analysed technique is a spatial decomposition:
−→v i = −→v i +−→v ′i (2.9)
where −→v i is the spatial average velocity in the point i, which is calculated around the point i in a certain moment of time, and −→v ′i is the spatial fluctuation in the same point. In fig. 2.8 spatial fluctuations of the previously depicted instantaneous flow fields are shown. In the left figure two structures are detected. In the right figure four rotational structures can be seen. The spatial decomposition depends on the surface around the point i. The surface should have a size equal to the largest length scale, which should be visualised. If the surface is smaller than a flow structure, the spatial average flow field is noisy and the structure can hardly be recognised. If the surface is too large the flow field is smoothed out together with smaller structures (low pass filter). In this case five neighbouring points are used to calculate spatial fluctuations.
From these examples it can be concluded that the extraction (eduction) of flow structures is not identical. The number and shape of structures depend on the chosen
18 Experimental Set-Up
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0
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1
X [ ]
Y [
(a)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0
0.2
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0.6
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1
X [ ]
Y [
(b)
Figure 2.8. Flow fields of spatial fluctuations. a) Two rotational structures are visualised, b) four vortices can be seen. The dimensions are normalised with the hole diameter d and the free-stream speed u∞. The leading edge of the hole is located at X = 0.
method. Despite this fact the largest structures are detected with all methods. All these methods are more or less successful in flow visualisation and they will be used in this work.
The aforementioned methods are subjective and can not be used for an automatic detection of vortical structures. To quantify and identify a vortex in a flow field the velocity field need to be analysed. An accepted definition of a vortical (rotational) structure or simple vortex is still lacking. I accept the global definition proposed by Lugt [46], that says: ‘a vortex is a multitude of material particles rotating around a common center’. Many algorithms for the vortex identification have been proposed. Among many I chose three of them based on Reynolds decomposition and vorticity, a positive second invariant of the velocity gradient tensor and an analogy to the rigid body motion. The two instantaneous flow fields, shown in fig. 2.5, are used to depict and explain the techniques, which are applied to detect vortices in PIV measurements.
The vorticity is −→ω = curl(−→v ). The normalised vorticity perpendicular to the measurement plane is calculated as:
z = d
u∞ ( ∂vy
∂x − ∂vx
∂y ) (2.10)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0
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X [ ]
Y [
−20
30
(a)
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Y [
−20
−20
(b)
Figure 2.9. The vorticity fields. The jet is perpendicularly injected into the cross- flow, which comes from left. The dimensions are normalised with the hole diameter d and the free-stream speed u∞. The leading edge of the hole is located at X = 0.
2.4 Flow fields and identification of vortices 19
and it is shown in fig. 2.9. It is obvious that besides the vortical structures the shear layer, formed at the hole trailing edge (X = 1), is also educed. Therefore, the vorticity of the Reynolds decomposed flow field is more appropriate to identify vortical structures. The Reynolds decomposition can be applied on the vorticity, too:
−→ω = −→ω +−→ω ′ (2.11)
where −→ω is the vorticity of the instantaneous field, −→ω is the average vorticity and −→ω ′ is the vorticity of fluctuations.
The fluctuation part of the vorticity can be normalised and calculated as:
′z = d
) (2.12)
Vortical structures educed with the fluctuation vorticity are depicted in fig. 2.10. Besides the vortical structures, vorticities and centres are shown. If a vortex boundary
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0
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(a)
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Y [
(b)
Figure 2.10. The fluctuation vorticity field. Stars represent the centres of vortices and numbers depict the average vorticity.
would be known its area can be easily calculated. Since this is not the case the threshold must be defined. When the threshold is known, vortical structures can be educed and their surface can be calculated as:
aω = ∫
A
da ≈ ∑
ai = Na (2.13)
where ai is the surface of the grid cell. In our case it is constant and denoted as a. N is the number of cells detected inside the vortex. If the area of the vortex is known its centre can be defined as:
−→rc =
aω (2.14)
In the two-dimensional case with discrete data the centre position can be calculated as:
xc = ∑
xi
20 Experimental Set-Up
Hence, vortices can be detected using Reynolds decomposition and vorticity. The calculation of vorticity requires a fine grid, which is not always possible to obtain with PIV. The measurement data contains also noise which can bring difficulties into determination of the threshold. Above all a shear layer, which does not represent vortical structures, is detected.
As an alternative Hunt et al. [32] defined a vortex as a positive second invariant of the velocity gradient (vij = ∂ui/∂ej) with lower pressure than in the ambient value (for more see Jeong and Hussain [34]). The second invariant Q is:
Q =
v11v12
v21v22
v22v23
v32v33
(2.17)
To identify vortices in a two-dimensional flow field the simplified expression can be used:
Qxy = ∂ux
∂x > 0 (2.18)
In fig. 2.11 vortices detected by means of the Q criteria are shown. Although, the second invariant criteria identifies vortices it suffers from derivatives and signs. Ve- locity derivatives must be calculated to estimate Q and the direction of the rotation is not determined.
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(b)
Figure 2.11. Vortices detected with the Q criteria (second invariant). Their central points are also shown.
The third method is the slightly modified gamma (Γ) method, which has been described in Graftieaux et al. [19]. The method is based on a rotation of a rigid body. Let us imagine that a vortex consists of small fluid lumps, which rotate around the vortex centre as rigid bodies. Then the normalised velocity moment can be calculated. If we are in the centre C of a vortex and we observe points, which belong to an interrogation area around C, than the average value of all normalised velocity moments should be 1. If we move out of the centre this value reduces. Graftieaux et al. [19] have proposed that all points with Γ larger than 2/π can be accepted as a part of a vortex. The normalised average velocity moment is defined as:
Γ(C) = 1 a
sin Mda (2.19)
where M is a point that belongs to the interrogation area around the centre C. The velocity of M is denoted with −→v M , −−→CM is the radius vector and M is the angle
2.4 Flow fields and identification of vortices 21
between them. ⊗ and | | are the product and modulus of vectors. This method is based only on the flow kinematics and does not require any derivations, which makes the method very applicable for PIV measurements. The threshold is very stable and the vortex direction is defined with the sign of Γ. Since we follow the vortex the local mean convective velocity −→v c estimated on the interrogation area around the point C is subtracted from instantaneous velocities in that area. The expression for calculating Γ is:
Γ(C) =
where −→vc = 1 NC
∑−→vMi and NC is the number of nods in the interrogation area
around the point C. The results achieved with this method are shown in fig. 2.12.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0
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Y [
(a)
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Y [
(b)
Figure 2.12. Vortices detected with the gamma criteria using the threshold of 0.7. The centres are also shown.
In fig. 2.10, 2.11 and 2.12 the two flow fields are presented. In the left flow field two or three vortical structures are detected. In the flow field, shown at the right-hand side, four or five vortical structures are educed. The vorticity plots of instantaneous flow fields show vortical structures and a shear layer. The Reynolds decomposition of the vorticity educes only vortical structures but in contrast to two other methods it generates a negative vortex upstream of the hole, which is probably just noise. This is a good and logical method, but a calculation of gradients is rather sensitive. Therefore, this method strongly depends on the quality of measurements and chosen thresholds. Q method does not depend on a threshold but it does not show the sign of the rotation.
To compare these methods closely, the vortex pair from the field located at the right-hand side is zoomed in and shown in fig. 2.13. The most regular pattern is achieved with the gamma method. The vortex core is almost circular. Results of the vorticity method strongly depend on the chosen threshold. The vortex centres are detected at similar positions in all cases, but the size of the vortex varies. In fig. 2.13c the vector plot represents the instantaneous velocity. The vortex is overshadowed by the cross-flow. If we apply the Galilean transformation (subtract convective velocity, see fig. 2.13d) the vortex becomes visible. The Galilean transformation is a powerful tool if one velocity component is dominant for example in a boundary layer. But in
22 Experimental Set-Up
cases with a strong two-dimensional shear lyer it is difficult to achieve a good result. The spatial decomposition is presented in fig. 2.13b. The spatial decomposition gen- erates a field comparable to the most common method, the Reynolds decomposition, which is depicted in fig. 2.13a. This method detects large vortices but it has a ten- dency to educe weak (ghost) structures, which are not detected by other methods.
1 1.1 1.2 1.3 1.4 1.5 1.6 0.3
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Y [
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0.4
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Y [
(d)
Figure 2.13. The different methods used to detect vortices in the flow field visualised together with the vector plots. a) The Reynolds decomposition with the vorticity of fluctuations in the background. b) Spatial fluctuations and vortices educed by means of the gamma method. c) The instantaneous velocity field with the instantaneous vorticity. d) The second invariant method (Q > 0) and the Galilean transformation with the local mean.
In this thesis mostly the gamma method coupled with vorticity calculations is applied to identify vortical structures.
2.5 Liquid crystal thermography
Liquid crystal thermography has been used for measuring temperature on the plate wall. To undertake these measurements two coated polyester sheets of thermochromic liquid crystals (TLCs) were glued on the plate wall around the hole and downstream of it (see figure 2.14). To minimise the leakage of the TLCs out of the sheets the
2.5 Liquid crystal thermography 23
black vinyl tape was glued around them. The TLC sheets have been produced by Hallcrest (R20C5W). The red colour should start at 20o and the bandwidth is 5oC. Measurements were conducted using the whole range of temperature dependent colors (wide band technique). The temperature in the channel was measured by means of a mercury thermometer with an accuracy of 0.05oC. The temperature in the channel was measured just before the beginning of each experiment. The jet temperature was adjusted and measured with the same thermometer to eliminate the bias. Images of the TLC sheets were taken with an analog three CCD video camera (JVC KY-F30). The camera was placed above the channel to look perpendicularly at the sheets. A light source was located at the side of the channel. To reduce reflection from the channel wall, the sheets were illuminated at an angle of approximately 45o. Each measurement was being conducted for 60 seconds and stored on a video tape by means of a S-VHS VCR (Panasonic AG-7350). All measurements were digitised using an analog video capture card (Pinnacle DC10) and saved in the non-compressed RGB format with a resolution of 720 x 580. A typical image is shown in fig. 2.16a. The line, which separates the two TLC sheets, is smoothed away by means of interpolation around it. The corrected image is depicted in fig. 2.16b. An ensemble of 1400 images per measurement is used for the statistical analysis.
Figure 2.14. The set-up used to conduct liquid crystal thermography.
Calibration of liquid crystals
Since the light distribution over the sheets and crystals themselves were not homo- geneous a calibration was conducted in situ by heating water in the channel. The camera and light source were in the same position during the measurements and cal- ibration process. The temperature step during calibration was 0.2oC and 400 images were captured per calibration step. To calibrate liquid crystals the RGB space must be transformed to the HSI space (see appendix B and for more details Gonzalez and Woods [18]). The hue value is calculated from the RGB space using:
hue =
} ; g − b ≥ 0
} ; g − b < 0
(2.21)
where R, G and B are normalised with a maximal value of red, green and blue colour (for 8 bit precision, which is valid in this research, the maximal value is 255). The hue distribution over the measured surface is shown in fig. 2.16c. The hue value is calibrated versus the temperature.
24 Experimental Set-Up
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20
21
22
23
24
25
26
27
Hue [ ]
T em
pe ra
tu re
[o C ]
Data Fitting 1 (part A) Fitting 1 (part B) Fitting 2
(a)
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Maximal error 1 Maximal error 2 Averaged error 1(b)
Figure 2.15. The calibration and its uncertainties. a) One calibration curve fitted with the wiggly eight order polynomial is marked as fitting 2. Better accuracy is achieved if the data are split in two parts and then fitted (curves fitting 1 part A and B). b) The maximal and average relative errors (in respect to the maximal difference of 6 degrees) calculated by reproducing calibration data obtained at different times t1 and t2.
Figure 2.15a depicts the typical wide band calibration curve hue versus temper- ature. Because of the steep gradient in the region of the blue colour the calibration curve is divided in two parts: from the beginning of the red colour (20oC in our case) till the first part of the blue range (23oC). The first part of the curve is fitted with a third order polynomial. The rest of the blue range is fitted by means of a fifth order polynomial. In this way the wiggle, which would have been produced if the eight order polynomial fitting had been applied on the full band at once, is avoided and the fitting error is reduced to a minimum. Because of the non-homogeneous TLCs and illumination over the sheets surface (see Sabatino et al. [57]) a full size image is divided into small interrogation areas of 2 x 2 pixels. For each interrogation area the calibration curve is calculated. The relative errors are depicted in figure 2.15b. The calibration curves are used for recalculating the temperature from the calibration data. This temperature is compared with the temperature measured by means of the mercury thermometer. The relative errors are calculated using the maximal temper- ature difference of 6 degrees between the jet and cross-flow temperatures. The curve named as maximal error 1 in figure 2.15b represents the maximal relative errors of the fitting method. The maximal relative errors are lower than 1% for temperatures between 20oC and 24oC. In the dark blue zone (temperature larger than 24oC) the errors increase and at the crystal limit, in our case 25oC, it reaches 2%. Before the red starts and when the blue colour is saturated the error rapidly increases. The average errors, labelled as average errors 1 in figure 2.15b and calculated using 1000 points, are lower than 0.4% for the whole range of the liquid crystals. To check the aging and effect of the camera position a small experiment was conducted. One week after the initial calibration the camera was slightly realigned to simulate a small change in illu- mination or camera position. The crystals were recalibrated and the new coefficients are used for the temperature recalculation in combination with the old data.
2.5 Liquid crystal thermography 25
1
2
3
4
20
21
22
23
24
−1
0
1
X [ ]
Z [
0.1 0.30.4
0.2 0.60.7
+1/25t 0 +2/25 +3/25 +4/25 +5/25 +6/25 +7/25 +8/25 +9/25 s
(a)
(b)
(c)
(d)
(e)
(f)
*
Figure 2.16. Liquid crystal thermography conducted with the perfect hole at the velocity ratio of 0.50. a) An instantaneous RGB raw image and b) corrected image of the thermochromic liquid crystals. c) hue values calculated out of the raw RGB image. d) The temperature distribution and e) the film cooling effectiveness for the given image. f) The time response of TLCs. * ) The vinyl tape used to protect edges of the TLC sheets.
26 Experimental Set-Up
The maximal errors generated through this process are shown in figure 2.15b as the curve maximal error 2. In the gradual part of the calibration curve, position and aging do not increase the relative errors but in the steep part (T > 23oC) the errors are much larger. Therefore, the camera, light source and crystals should be in the same position during the calibration and measurements and also the time difference between the calibration and experiments should not exceed a few days. Otherwise the system should be recalibrated or the steep part of the calibration curve should be avoided. The calibration accuracy is within 0.1 degree in the red-green zone and within 0.3 degree in the dark blue zone.
Effectiveness and uncertainties
Using calibration hue values, depicted in fig. 2.16c, are transformed into the temper- ature field shown in fig. 2.16d.
The plexiglas surface can be treated as an adiabatic wall. Therefore, the effective- ness is calculated from the measured temperature using equation 1.8:
η = T∞ − Tf
T∞ − Tj
A typical contour plot of the calculated effectiveness is presented fig. 2.16e. From equation 1.8 the uncertainty of the adiabatic film cooling effectiveness can
be calculated as
∂T∞ T∞)2 (2.22)
Temperatures of the jet and cross-flow have been measured with the same thermome- ter. Therefore, the uncertainty Tj = T∞ = 0.05oC. If the uncertainty of the wall temperature is written as Tf = nTj , we obtain the following equation for the adiabatic film cooling effectiveness:
η = T∞
Tj − T∞
(Tj − T∞)2 (2.23)
η has maximum values for Tf = Tj or Tf = T∞ which gives
ηmax = T∞
Tjet − T∞
√ 1 + n2 (2.24)
The uncertainty of the effectiveness, measured in this way depends on n, which rep- resents the quality of the calibration. For n = 1, η is 0.012 and for n = 6, η is 0.051. n is around 2 of the gradual part of the calibration curve and reaches 6 for the steep side. Therefore, the absolute effectiveness error is 0.02 for 0 < η < 0.65 and η = 0.05 if η > 0.65.
The documented time response of TLCs is between 0.01 and 0.1 s. To check this, TLCs were placed in the test section. The temperature of the main stream in the test section was 19.7oC, which means that the colour of the crystals was black. The TLCs were suddenly exposed to the hot jet, which temperature was 26oC. Their reaction is depicted in fig. 2.16f. The sequence of images shows the colour changes on each
2.6 Perfect and imperfect holes 27
of them. Taking into account that the sampling frequency of the camera was 25Hz, I conclude that sheets of TLCs placed in water react with a higher frequency than 25 Hz, which gives a reaction time shorter than 0.04 s.
Buoyancy effect
The jet temperature is 26oC and the cross-flow has a temperature of 20oC. The Richardson number, defined here as Ri = gβdT
u2∞ , is 0.015 which means that the
buoyancy forces can be neglected and the heat transfer is dominated by forced con- vection. In the equation g is the acceleration in the gravitational field, T is the difference between the jet and cross-flow temperatures and β is the thermal expan- sion coefficient. The Richardson number based on the jet velocity is proportional to the above defined Richardson number. The proportionality factor is 1/(V R)2, which gives the highest Richardson number of 0.25 for V R = 0.25. This means that the buoyancy forces can have a small influence on secondary flow structures inside the jet at low velocity ratios. In a gas turbine and/or in a Ludwieg tube, velocities are much higher and the gravity effect totaly vanishes (Ri < 10−4).
2.6 Perfect and imperfect holes
(a) (b)
Figure 2.17. a) The shape and dimensions of the symmetrical and asymmetrical imperfection. b) The outlet of the jet hole and the position at which the imperfection can be placed. The half-torus placed at the exit of the hole is called here inner-torus 1. Inner-torus 2 is the imperfection at the second position and inner-torus 3 is the deepest positioned imperfection.
A set of experiments has been performed with a perfect hole. The perfect hole is a smooth hole, which does not contain any imperfections. These results are used as a benchmark. Thereafter, experiments with imperfect holes have been conducted. These experiments are named here as inner-torus or imperfect experiments. An im- perfect hole represents a film cooling hole, which contains a production imperfection. An imperfection inside the film cooling hole, generated by means of laser drilling, is often discrete and it has a toroidal shape (see von Allmen and Blatter [67]). It is rel- atively big with a length scale which can exceed a quarter of the hole diameter. Since melted material, which is resolidified inside the hole, forms a discrete quasi-toroidal imperfection (see fig. 1.3b and 1.3c), I use in this research a half-torus to simulate
28 Experimental Set-Up
the production imperfection. The torus is a body, which emanates from rotation of a circle around the torus axis. If the flat shape is a rectangle or triangle instead of the circle the toroidal object is called here rectangular- or triangular-imperfection (see fig.2.18b). Now, I can define the half-torus as a body formed by the intersection of a cylinder and a torus of the same radius. The radius of the cylinder and the torus is constant in all experiments and it is equal to d/2, where d is the diameter of the hole used in experiments.
Particle image velocimetry and laser induced fluorescence are used for visualising and quantifying flow fields. The main experiments are performed with the perfect hole and two imperfect holes. The investigated imperfect cases are inner-torus 1 and inner-torus 2. In these cases the hole contains a half torus (number 3 in fig. 2.18a) at the first and second positions inside the hole (see fig. 2.17b), respectively.
(a)
(b)
Figure 2.18. a) Different sizes of the half-torus imperfection. b) Three shapes of the imperfection: 1 - half-torus, 2 - rectangular (symmetrical) imperfection and 3 - triangular imperfection.
The hole geometry can be immensely varied. To study the effect of different im- perfections on the adiabatic film cooling effectiveness, I change the position, shape, size and symmetry of the imperfection. The temperature on the adiabatic wall has been measured by means of liquid crystal thermography. To investigate the influence of the imperfection position the half torus, depicted as number 3 in fig 2.18a, is fixed at three different depths inside the hole (see fig. 2.17b). To study the dominance of the imperfection and the effect of the multiple hole imperfections the three similar half toruses are simultaneously fixed inside the hole. This case is named here ‘triple’ imperfection. The influence of the blockage is examined at the second position (po-
2.6 Perfect and imperfect holes 29
sition 2 in fig. 2.17b) with the five circular imperfections shown in fig. 2.18a. The blockage of the imperfection is altered by changing the diameter of the torus cir- cle. To answer the question: ‘How does the shape of a discrete imperfection bear on the effectiveness?’, the half-torus imperfection is compared with the rectangular- and triangular-imperfections (see fig. 2.18b). The size of the characteristic cross-sectional shape of the toroidal imperfection is chosen in such a way to obtain constant blockage (B = Ablocked/Ahole, where A is the area) at the smallest cross-section. The geom- etry and dimensions of the symmetrical and asymmetrical imperfection are sketched in fig. 2.17a. The asymmetrical imperfection is fixed at the second position. A cres- cent (blockage) location of the asymmetrical imperfection determines the name of the investigated case. If the middle of the crescent is oriented towards the windward side the name is the windward imperfection. Following the same logic, the lee and right-hand imperfections are cases in which the crescent is at the lee and right-hand side respectively.
30 Experimental Set-Up
3.1 Introduction
Literature, which covers a jet in a cross-flow, is very extensive. The problem is relevant to many physical and engineering processes. Film cooling is characterised by ‘weak’ jets, which are ejected into the cross-flow boundary layer through inclined holes. Therefore, I focus only on an inclined jet in a cross-flow with modest velocity ratios V R ≤ 1.50.
The idea of coherent structures is very old. Some flows are heavily dominated by a large vortical motion, which can be treated as a coherent motion. The literature overview has been given in section 1.4. Here a synopsis of the most important works is given. Haven and Kurosaka [26] investigated experimentally the counter rotating vortex pair (CVP) and anti-CVP. Different hole shapes have been investigated. They postulated that CVP originates at the side rims of the hole and they named it as steady kidney vortices. They have also discovered a double-decked structure. Two unsteady vortices roll above steady kidney vortices. According to the sign of their rotation these vortices can be unsteady kidney or unsteady anti-kidney vortices. They depict a heuristic model, capable to explain the flow field. Lim et al. [44] investigated coherent structures of the jet in a cross-flow experimentally. They concluded that the cylindrical vortex sheet emerged from the hole underwent three distinct folding processes. One process leads to a formation of CVP and the other two form windward and lee vortices. These three vortical structures are independent. New et al. [51] have formulated the folding process in details. This paper mentions multiple scenarios of vortical rolls. The type and way of roll depend on the aspect ratio (hole shape) and MR (or V R). The jet ejected through a short hole has been studied by Peterson and Plesniak [54]. A special attention has been put on the plenum orientation and its influence on the flow field. They investigated the jet cross-flow velocity field by means of PIV. The aforementioned structures have been visualised and quantified. Two steady vortices have been detected downstream of the hole. They have been named downstream spiral separation nodes, according to the flow topology. Guo et al. [23] carried out a large-eddy simulation of the jet in cross-flow recently. The numerics has been able to detect large vortical structures reported in previous experimental works.
In fig. 1.5, the reported vortical structures are depicted. To validate the existence of these structures and to investigate the influence of an imperfection, the measure- ments were conducted in the water channel with the set-up described in section 2.3. In this chapter results of PIV and LIF measurements are presented. In section 3.2, the boundary layer and characteristics of the submerged jet are examined. It will be deduced that the flow field is dominated by four large vortical structures (see
32 Flow Field Characteristics
Figure 3.1. Sketch of vortical structures generated by the jet cross-flow interaction which are detected in my experiments.
fig. 3.1). To detect and measure windward and lee vortices, two-dimensional velocity measurements were conducted along the central plane. Preliminary results are pub- lished in my article Jovanovic et al. [36] and the complete central plane experiments are studied in section 3.3. Measurements along horizontal planes, which are analysed in sections 3.4, reveal that the spiral vortices are generated just downstream of the hole trailing edge. The largest vortical structure produced by a jet injection into a cross-flow is the counter rotating vortex pair. These vortices are educed out of the lateral measurements. The results are examined in section 3.5. At the beginning of each section the flow field generated by means of the jet injected through the perfect hole is depicted. After that the influence of the imperfection is shown and compared to the perfect case.
3.2 Jet and cross-flow properties
3.2.1 Cross-flow boundary layer on flat plate
0 20 40 60 80 100 120 140 160 180 200 0
5
10
15
20
25
30
35
40
45
50
(a)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0
2
4
6
8
10
12
14
16
18
20
22
24
37x37mm2
(b)
Figure 3.2. The boundary layer profiles of the cross-flow. a) The comparison of time and spatial averages with the 1/7 law. b) Non-dimensional profiles and the influence of the PIV image size on them. Cy = y
√ u∞/νx and Vx = vx/u∞
3.2 Jet and cross-flow properties 33
A first step in this investigation is to analyse the properties of the jet and cross- flow. Main cross-flow properties are the state and size of the boundary layer and the free stream velocity. The free stream velocity was measured many times to determine repeatability. It is found that in different experiments the free stream velocity varies from 185 mm/s to 205 mm/s. This variation has been influenced by the low quality of butterfly valves. These valves have been used for adjusting the velocity in the test section and they cannot be precisely positioned. Therefore a set of comparable experiments was performed under the same conditions. The comparable experiments have a similar free stream velocity, which variation of 4% is within the confidence interval of PIV. In all measurements the value of 200 mm/s is used for normalising. The turbulence intensity of the free stream is around 2%.
In fig. 3.2 the boundary layer profile is presented. The boundary layer is turbulent. The leading edge of the flat plate triggers the boundary layer. The turbulent boundary layer of the cross-flow can be described by the 1/7 law and expressed as: vx(y)/u∞ = (y/δ)1/7, where vx(y) is the average velocity along the streamwise coordinate x and it depends only on y, δ is a boundary layer thickness. The time average and spatial average profiles measured 1225 mm from the plate leading edge are shown in fig. 3.2a. It can be seen that the time average velocity, obtained by averaging 1000 PIV data at one X position, agrees very well with the spatial average data around the position X from independent samples. Therefore, the problem can be treated as ergodic.
The 99% boundary layer thickness (δ99) is a distance from the plate wall at which the boundary layer velocity reaches 0.99u∞ and it is 39 mm (0.68d) at X = 21.5. The boundary layer can be depicted with normalised values of Vx(y) = vx(y)/u∞ versus Cy = y
√ u∞/νx (see fig. 3.2b). In the same figure the boundary layer measured
with two image sizes are compared. It can be seen that the agreement is within the accuracy of PIV. The smaller windows give the better resolution in the vicinity of the wall and it leads to a similar estimation of the boundary layer, displacement and momentum thickness. Displacement thickness δ∗ =
∫∞ o
(1 − (vx(y)/u∞))δy is 6.2 mm and momentum thickness θ =
∫∞ o
(1 − (vx(y)/u∞))(vx(y)/u∞)δy is 4.4 mm. Similar values measured 1550 mm from the plate leading edge have values of δ∗ = 6.5 mm and θ = 5.0 mm.
3.2.2 Main characteristics of submerged jet
Submerged jet through perfect hole
A submerged jet or free jet is a jet injected into a steady surround. In this section only the jet profiles and turbulence intensities are analysed. The detailed discussion is given in appendix C. Data are presented in coordinate system abz, which is aligned with the axis of the hole pipe (see fig. C.1).
In fig. 3.3a jet profiles of the perfect hole are shown. They have been extracted within the interval of 79 mm ≤ a ≤ 82 mm around the line A = 1.4. The profiles are depicted at different Reynolds numbers 0.3, 0.6, 1.1 x 104. It can be seen that the profiles are almost flat. A small deviation is detected in the vicinity of the leading edge (B = 0). The jet Reynolds numbers are larger than the critical Reynolds number (Rec = 2300 for the cylindrical pipe), hence small disturbances (such as a state of the flow straightener and alignment of pipes) lead to transition and a turbulent
34 Flow Field Characteristics
0
0.2
0.4
0.6
0.8
1
1.2
B [ ]
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
B [ ]
(b)
Figure 3.3. Va profiles of the submerged jet a) in the perfect case at three Reynolds numbers and b) at the Reynolds number 1.1 x 104 generated by three geometries. Velocity profiles have been extracted around the line A = 1.4. The velocities are normalised by u∞ = 200 mm/s, which is the velocity of the cross-flow that will be superimposed on a submerged jet.
flow. Although the length of the pipe is 10 times larger than the diameter, the flow cannot fully develop. Therefore, the small profile deviation is probably an effect of the non-developed turbulent flow and it is partially influenced by the jet deceleration at the leading edge. At Re = 1.1 x 104 the relative difference between the maximal and minimal values detected at the plateau is 4% with the potential core velocity vcore
a ≈ 225 mm/s. Vb profiles are negligible and their values are within the PIV uncertainty. In fig. 3.3 profiles va are normalised by u∞ = 200 mm/s, which is the free stream velocity that will be superimposed on submerged jet.
To check the jet characteristics along the outlet of the hole the measurements were conducted in the horizontal plane Y = 0.15 with the perfect hole. The results are presented in fig. 3.4. The Reynolds number is 10% smaller than in the above analysed case and it is equal to 1.0 x 104. The core velocity along the x direction vcore
x is 161 mm/s and vz ≈ 0. Results are obtained by averaging 250 PIV data in each point. It can be seen that the potential core along the x axis is homogeneous with a turbulence intensity of 5% along the same axis.
0 0.5 1 1.5 2
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
X [ ]
Z [
0.8
0.8
(a)
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
X [ ]
Z [
12
12
4
4
(b)
Figure 3.4. Horizontal slice through the jet at Y = 0.15 at Re = 1 x 104: a) Vx = vx/200 mm/s and b) 100 ∗ rms(vx)/vcore
x [%]
3.3 Jet cross-flow interaction along central plane 35
It can be concluded that the jet is turbulent with the turbulence intensity of 5−6% in all directions at the exit of the hole. Large vortical structures and pulsations inside the jet have not been detected (see fig. C.2). The jet cross-flow interaction is investigated by injecting the turbulent jet into the turbulent boundary layer.
Submerged jet through imperfect holes
Inner-torus 1, placed at the hole exit, and inner-torus 2, located 1.2d inside the hole (see fig. 2.17b) were placed inside the hole to conduct experiments of the submerged jet through imperfect holes. In this section only the velocity profiles extracted around the line A = 1.4 are presented in fig. 3.3b. The velocity gradients are almost the same for all three cases above the hole trailing edge (B = 1) but they deviate above the hole leading edge (B = 0). The hole leading edge is blocked by inner-torus 1 and the jet is accelerated. The flat profile detected in the perfect case is reshaped to almost parabolic one. Inner-torus 2 is located deeper inside the hole. Therefore the jet can reach the hole leading edge and the jet outlet profile is in between the perfect and inner-torus 1 profiles.
The analysis of other statistical values of the submerged jet is given in appendix C. Main conclusions are that turbulent kinetic energy values are rather small in the perfect case at the hole exit. Inner-torus 1 generates turbulent kinetic energy of 30% above the leading edge imperfection. In the case of inner-torus 2 lower values, up to 15%, are detected on the same spatial position. Turbulence stresses are 4 − 5 times larger in the inner-torus 1 case than in the perfect case. Inner-torus 2 generates stresses which are 2 − 3 times greater than in the perfect case. In the case of inner- torus 1 the small portion of the potential core is not influenced by the turbulence produced at the imperfection. In the inner-torus 2 case, the whole jet is disturbed and the turbulence transport cannot be neglected. Instantaneous structures are larger and stronger than in the perfect case and they are the product of the imperfection inside the hole.
3.3 Jet cross-flow interaction along central plane
3.3.1 Visualisations and central plane borders
The cross-flow with the free stream velocity u∞ ≈ 200 mm/s is superimposed on the submerged jet. Therefore, the jet is deflected and pushed towards the plate surface. The radius of the bend depends on the momentum ratio. The jet cross-flow interaction with film cooling characteristics (V R < 2) forms two main zones: an undisturbed zone of the free stream and a cooling volume. These two zones are separated with a shear layer. To pinpoint the border between the zones LIF visualisations wer