Unsteady Characteristics of Laminar Separation Bubbles; An Experimental and Numerical Investigation

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UNSTEADY CHARACTERISTICS OF LAMINAR SEPARATION

BUBBLES

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UNSTEADY CHARACTERISTICS OF LAMINAR SEPARATION

BUBBLES

AN EXPERIMENTAL AND NUMERICAL INVESTIGATION

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus Prof. dr. ir. J.T. Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen

op dinsdag 21 december 2004 om 13.00 uur

door

Marco BARAGONA

Ingegnere aeronautico, Università degli Studi di Roma, Italië geboren te Roma, Italië

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Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof.dr.ir. P.G. Bakker Technische Universiteit Delft, promotor Prof.dr.ir. M.J.L. van Tooren Technische Universiteit Delft, promotor Dr.ir. H. Bijl Technische Universiteit Delft, toegevoegd Prof.dr. A.E.P. Veldman Rijksuniversiteit Groningen

Prof.dr.ir F.T.M. Nieuwstadt Technische Universiteit Delft Prof.dr.ir. J.L. van Ingen Technische Universiteit Delft Ir. D.M. Passchier Technische Universiteit Delft

Published and distributed by: DUP Science DUP Science is an imprint of

Delft University Press

Faculty of Aerospace Engineering P.O. Box 98 2600 MG Delft The Netherlands Tel: +31 15 2785678 Fax: +31 15 2785706 E-mail: info@library.tudelft.nl ISBN 90-407-2566-7 Copyright c° 2004 by M. Baragona.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher.

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vii

Summary

Laminar separation bubbles may occur in a wide range of engineering applications such as turbomachinery flows, wind turbines, hydrofoils etc. Much attention has been given to their effect on the flow over airfoils because of the importance for an accurate prediction of lift, drag and heat transfer.

In the aeronautical world, laminar separation bubbles have traditionally been of con-cern for the aerodynamics of sailplanes and of small aircrafts. However, recent mea-surements stress their importance for commercial transport aircrafts in slow flight, where laminar bubbles strongly affect the flow on high-lift devices.

In spite of their importance for the global characteristics of the flow, the prediction of the behavior of laminar bubbles is still not satisfactory, especially close to stall conditions.

The main objective of this thesis is to investigate the unsteady features of laminar separation bubbles with the ultimate goal of an improved prediction of their behavior during the design process, especially close to stall conditions.

This objective was defined during the first part of the investigation, when the stalling behavior of a multi-element slotted high-lift configuration was analyzed. The exper-imental investigation of this multi-element configuration clearly showed the impor-tance of a correct prediction of the bursting of the bubble present on the flap. This bursting determined in fact the stalling characteristics of the whole configuration. Existing design tools proved inadequate to the task of predicting bursting occurrence. Furthermore, Navier-Stokes calculations of the multi-element configuration showed that unsteady effects were crucial in order to predict successfully the behavior of the bubble.

However, these unsteady effects could not be investigated in detail on the multi-element configuration. A ”simplified” setup was then considered that allowed to investigate the flow characteristics in great detail while retaining the same local phys-ical characteristics of its ”real” counterparts. A large separation bubble was induced on a flat plate through a sudden pressure drop. This setup effectively reproduced the flow conditions in the boundary layer of an airfoil in the area where the laminar separation bubble is located by matching quantities like ReθS and pressure gradient.

However, this was realized at much larger length scales so that the bubble was large enough to allow accurate measurements.

These measurements were carried out using the Laser Doppler Anemometry and Par-ticle Image Velocimetry optical techniques. The combined use of both techniques, allowed to achieve a much broader insight into the flow characteristics than what would have been possible by using just one of the two.

A strong shedding of vortical structures was found to characterize the bubble behavior and the transition process as well as the turbulent boundary layer developing behind the bubble. The characteristics of the turbulent boundary layer were strongly affected by the upstream history. The behavior of the transition region and of the first part of the turbulent region appeared to be crucial to the present flow field. In these regions, the shedding was found to be strongest.

To further investigate the physics involved and to extend the experimental results to untested velocities and pressure gradients, numerical computations were carried out on the same ”simplified” setup. The experimental data were reproduced and a

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num-computations in order to reproduce the experimental evidence was investigated. It is found that, although shedding also appears when disturbances are not introduced, appropriate ”forcing” is needed in order to obtain realistic bubbles. A parametric analysis was carried out to reveal the dependance of the unsteady characteristics of the bubble on velocity and pressure gradient variations. For the change in time aver-aged quantities, known trends were confirmed.

Finally, the bursting process was investigated. A shift in Strouhal number was ob-served after bursting. This shift was found to be due to vortex pairing. The bubble was found to move towards an absolute instability when approaching bursting. How-ever, the change in stability could not be used as a criterion to predict bursting occurrence, mainly because of limitations in the stability theory. The semi-empirical criterion of Gaster was confirmed by the present results. However, if the disturbances present in the flow are unknown or poorly estimated, the criterion will fail just because the computed values of the relevant parameters will not be accurate enough.

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ix

Samenvatting

Laminaire loslaatblazen kunnen optreden in diverse technische stromingstoepassin-gen, zoals bij turbomachines, windturbines, draagvleugelboten enz. Veel aandacht is besteed aan hun effect op de stroming over draagvlakken, wegens het belang voor een nauwkeurige voorspelling van draagkracht,weerstand en warmteoverdracht.

In de luchtvaartwereld hebben laminaire loslaatblazen traditioneel in de belangstelling gestaan voor met name de a¨erodynamica van zweefvliegtuigen en kleine vliegtuigen. Recente metingen benadrukken echter hun belang voor commerci¨ele transportvliegtu-igen in langzame vlucht, waar de laminaire blazen de stroming rond high-lift devices (kleppen) sterk be¨ınvloeden.

Ondanks hun belang voor de algemene kenmerken en structuur van de stroming, is de voorspelling van het gedrag van laminaire bellen nog niet bevredigend, vooral indien de vleugelstroming zich dicht bij overtrekken bevindt. De belangrijkste doelstelling van deze thesis is de instationaire eigenschappen van laminaire loslaatblazen te on-derzoeken met het uiteindelijke doel een betere voorspelling van hun gedrag tijdens het ontwerpproces, vooral voor de situatie dicht bij overtrekken.

Deze doelstelling werd gedefinieerd tijdens het eerste deel van het onderzoek, toen het overtrekgedrag van een multi-element klepconfiguratie werd geanalyseerd. Het experimentele onderzoek van deze multi-element configuratie toonde duidelijk het belang van een correcte voorspelling van het barsten van de blaas aanwezig op de klep. Dit barsten bepaalde in feite de overtrekkenmerken van de gehele configuratie. Bestaande ontwerphulpmiddelen bleken ontoereikend om het barsten te voorspellen. Voorts toonden Navier-Stokes berekeningen van de multi-element configuratie aan dat instationaire stromingseffecten essentieel waren om het gedrag van de blaas met succes te voorspellen.

Deze instationaire effecten konden echter niet in detail worden onderzocht voor de multi-element configuratie zelf. Een ”gesimplificeerde” opstelling is daarom ontwor-pen, die toestond om de stromingskenmerken zeer gedetailleerd te onderzoeken, ter-wijl het dezelfde lokale fysische kenmerken van zijn ”echte” tegenhangers behield. Een grote loslaatblaas werd veroorzaakt op een vlakke plaat door een plotselinge drukdal-ing. Deze opstelling reproduceerde effectief de stromingssituatie in de grenslaag van een vleugel in het gebied waar de laminaire loslaatblaas zich bevindt, door groothe-den als ReθS en de drukgradi¨ent aan te passen. Nochtans werd dit gerealiseerd bij

veel grotere lengteschalen zodat de blaas genoeg groot was om nauwkeurige metingen mogelijk te maken.

Deze metingen werden uitgevoerd met behulp van de ”Laser Doppler Anemometry” en ”Particle Image Velocimetry” optische technieken. Het gecombineerde gebruik van beide technieken maakte het mogelijkk om een veel breder inzicht in de stromingsken-merken te verkrijgen dan bij het gebruik van slechts een techniek.

De sterke afschudding van wervelstructuren bleek kenmerkend voor het gedrag van de blaas en het omslagproces, evenals voor de turbulente grenslaag, die zich achter de blaas ontwikkelde. De eigenschappen van de turbulente grenslaag werden sterk be¨ınvloed door de stroomopwaartse geschiedenis. Het gedrag van het omslaggebied en van het eerste deel van het turbulente grensgebied leek essentieel voor het huidige stromingsveld te zijn. In deze gebieden bleek de wervelafschudding het sterkst te zijn. Om de fysica verder te onderzoeken en de experimentele resultaten aan te vullen voor

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bijzonder bleek het proces van heraanliggen van de stroming sterk te worden bepaald door de dynamica van de wervelstructuren. Voorts werd het controversi¨ele punt on-derzocht of de in de stroming aanwezige storingen al dan niet in de berekeningen moesten worden ge¨ıntroduceerd om het experimentele bewijsmateriaal te reproduc-eren. Hieruit bleek dat, hoewel wervelafschudding ook optreedt wanneer de storingen niet worden ge¨ıntroduceerd, een juiste ”forcering” vereist is om realistische blazen te verkrijgen. Een parametrische analyse werd uitgevoerd om de afhankelijkheid van de instationaire kenmerken van de blaas van snelheid en drukgradi¨entvariaties vast te stellen. Voor de verandering van tijdsgemiddelde grootheden werden de bekende tendensen bevestigd.

Tot slot werd het barstproces onderzocht. Een verschuiving in het Strouhal getal werd waargenomen na het barsten. Deze verschuiving is toe te schrijven aan het paren van wervels. De blaas bleek absoluut instabiel te worden naarmate het barsten naderde. Nochtans kon de verandering in stabiliteit niet als criterium worden gebruikt om het barsten te voorspellen, hoofdzakelijk wegens beperkingen in de stabiliteitstheorie. Het semi-empirische criterium van Gaster werd bevestigd door de huidige resultaten. Echter, als de in de stroming aanwezige storingen onbekend of slecht geschat zijn, zal het criterium falen enkel omdat de berekende waarden van de relevante parameters niet nauwkeurig genoeg zullen zijn.

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Introduction

1.1 Laminar separation bubbles

Laminar separation bubbles may occur in a wide range of engineering applications such as turbomachinery flows, wind turbines, hydrofoils etc. Traditionally, most at-tention has been given to their effect on the flow over airfoils because of the importance for an accurate prediction of lift, drag and heat transfer.

A separation bubble may occur when the laminar boundary layer reaches the separa-tion point before transisepara-tion to a turbulent layer is achieved. For each airfoil shape and thickness, this will happen at a certain combination of Reynolds number, freestream turbulence level T u and angle of attack α. For any airfoil at a relatively low turbu-lence level and a given α, there exists a value of the Reynolds number below which laminar separation occurs. The flow development after the separation point depends strongly on the behavior of the separated laminar shear layer. The traditional idea is that due to the high instability of this shear layer, transition to turbulence occurs shortly after the separation point, increasing the entrainment with the external flow and thus causing reattachment to the surface and the formation of a region of rela-tively stagnant flow, a short bubble (figure 1.1).

At high angles of attack or at low Reynolds numbers the flow may become unable to overcome the adverse pressure gradient and fail to reattach. The flow pattern will then change into a so called long bubble or into a completely separated flow (for airfoil flow: leading-edge stall). The difference between a long and a short bubble is controversial and difficult to define for any kind of flow condition. In the case of airfoil flows, however, the formation of a long bubble causes a global reorganization of the pressure distribution over the airfoil surface. The bubble effect on the pressure distribution is thus different in the two cases: local and limited in the case of a short bubble, more influential in the case of a long bubble.

1.2 Early studies on laminar separation bubbles

The existence of laminar separation bubbles was first recognized by Jones [44] who investigated their influence on the stalling process of airfoils. Gault [31, 55] further

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..

ture of a short laminar bubble [39].

investigated the bubble behavior close to stall conditions and, based on this inves-tigation, introduced a distinction between three types of stall, namely leading edge, trailing edge and thin airfoil stall [31]. However, the most notable advance in the understanding of bubble structure and behavior came with the work of Gaster [30] who investigated a large number of bubbles produced on a flat surface. The adverse pressure gradient was created by placing an airfoil in upside-down position above the flat plate. This configuration allowed Gaster to perform pressure and hot-wire measurements of many bubbles, realized for different Re and pressure gradients. Hor-ton [39] used Gaster’s results as well as the advances in laminar [82] and turbulent [80] boundary layer theory for his semi-empirical bubble model. This model was based on the classical view of the bubble outlined in section 1.1. Many more semi-empirical models have been proposed in the successive decades without, however, introducing any major improvement in the physical description of the bubble with respect to Hor-ton’s model. In section 1.3 some of these models are recalled when discussing bursting predictors.

Despite this effort, these semi-empirical models generally failed to predict the struc-ture of the bubble in all conditions and its behavior close to stall. This flaw clearly shows that the classical model of the bubble does not capture all the physics at play. In the last decade, most research efforts focussed on the unsteady characteristics of the bubble and on the influence of upstream disturbances, partially changing the classical view of the bubble. We will discuss these aspects in section 1.2.1.

1.2.1 The unsteady structure of the bubble

The shortcoming found in the numerical predictions of bubble behavior and of burst-ing onset, suggests that the modelburst-ing, if not the understandburst-ing of the physics involved, is still lacking.

In Horton’s model, the region where the flow reattaches to the surface was described as fully turbulent and any flow fluctuaction at separation and in the laminar part of the bubble was neglected. Especially at lower Re numbers, however, available exper-imental evidence shows that a different behavior should be expected.

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1.2. EARLY STUDIES ON LAMINAR SEPARATION BUBBLES 3

Gaster [30] first observed in his experiments that low frequency oscillations seemed to be a characteristic of low Re bubbles. These oscillations were especially strong in long bubbles; a patch of high- frequency turbulence formed intermittently in the early stages of transition, delaying the formation of a continuous turbulent signal to a position much more downstream than in the short bubbles he tested. Gleyzes [33] experimentally analyzed the transitional flow over the surface of an ONERA LC-100-D airfoil at a Reynolds number equal to 0.5 · 106 _{and higher. Flow visualisations}

showed the formation of well defined vortical structures in the rear region of the bub-ble present on the airfoil. These structures were seen to characterize strongly the first stages of turbulent boundary layer development and to be quite persistent in the ensuing turbulent flow as well. In both investigations, however, no additional efforts were made to understand better the relevance of these vortical structures to the characteristics of the turbulent boundary layer developing behind the bubble. No more recent experiments on the topic are known to the author. On the other hand, much experimental effort was directed to the study of instability and transition in the bubble [49, 22]. The mechanism of transition in a laminar bubble and the relevance of the level and nature of flow disturbances to the transition process are, however, still controversial. More recent experimental works on the topic, focusing on the unsteady structure of the bubble, will be discussed in section 3.1.

Due to the difficulty of measuring accurately the unsteady structures present in the bubble, the most notable advances in the comprehension of its unsteady features came, however, from numerical investigations, starting from the beginning of the 90’s. Pauley [64] reproduced numerically Gaster’s experiments using an unsteady laminar Navier-Stokes solver. She identified the above mentioned structures with the occurrence of vortex shedding originating from the separated laminar shear layer. Time averaging the unsteady results, Pauley found that the surface pressure distribu-tions matched Gaster’s findings and the streamlines showed the classical steady closed bubble pattern (see fig. 1.1). Similar numerical findings were reported for an Eppler 387 airfoil [64]. Though surprising, this is certainly possible since most experimental setups for static measurements (like the ones for the evaluation of airfoils design) are not able to sense unsteady variations occurring above a certain frequency, thus providing a ”hardware” filtering of the actual physical evidence. The same vortex shedding occurrence was later confirmed by the numerical results obtained by Tati-neni over the APEX airfoil [81].

The analyses of Pauley and Tatineni were two dimensional and neglected completely any small-scale turbulence effect. Their results clearly show, however, that the lam-inar part of the bubble is not a region of stagnant flow but rather a region where shedding of well defined vortical structures periodically occurs. These structures are expected to affect strongly the ensuing turbulent flow and the transition process. The customary assumption that transition occurs at the laminar separation point [54] is found inadequate in this context and the prediction of transition onset is much more challenging [63].

More recent numerical research focussed on instability and transition of laminar sep-aration bubbles by performing DNS on ”simplified” setups. These works will be described in section 4.1.

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as either the momentary breakdown (in case of long bubble formation) or definitive breakdown (in case of leading-edge stall) of the turbulent shear layer reattachment process. So in this model, bubble bursting can be defined as the failure of the turbu-lent shear layer reattachment process.

This model however fails in explaining the different flow patterns (thin airfoil stall and leading edge stall) resulting from the bursting of the bubble and to predict suc-cessfully bursting occurrence. The strongly unsteady structure of the bubble that was discovered by more recent research (see section 1.2.1), could be the clue to a better understanding of the problem. How the unsteady behavior influences the onset of bursting is, however, still unclear. In the early work of Pauley [62] it was suggested that the long bubble was steady and the small one unsteady. The end of the unsteady behavior would have marked the onset of bursting. This is, however, contradicted by more recent results from the same author [64, 99] where the shedding was found to be stronger in the long bubble than in the short ones. More recently, Alam [4] per-formed DNS calculations on a laminar separation bubble. He suggests that bubble bursting may mark the difference between a convectively unstable ”short” bubble and an absolutely unstable ”long” bubble, depending on the amount of reverse flow. They analyzed however only short bubbles and no conclusions could therefore be drawn on this suggestion. On the other hand, the DNS on a laminar bubble performed by [78] showed that an absolute instability was present, although the bubble was a small one. Whether bubble bursting is driven by a change in the stability characteristics of the bubble or by some global instability of the flow connected to the external potential flow [30] is still an open question.

In any case, the unsteady nature of the laminar separation in these conditions appears to be a crucial point to be taken into account for a proper analysis of the bursting problem.

1.3.1 Bubble bursting predictors

Most numerical codes for airfoil design purposes do not include any bursting predic-tion method. Several semi-empirical methods have however been proposed in the past to predict bursting onset. We shortly present them here for completeness. Neverthe-less, all of them substantially fail in predicting bubble bursting in all conditions and require a very accurate tuning to provide satisfactory results.

Based on experimental results on NACA 63-009 and 64-006 airfoils, Owen [59] first proposed a one parameter criterion for bursting. Bursting would occur whenever ReθS became less than 125. However, Crabtree [16] observed that bursting could

take place also at much higher values of ReθS and suggested the use of an

addi-tional parameter σ based on the pressure rise over the bubble, defined as: σ = (Preattach− Pseparation)/0.5ρUS2. In this criterion, bursting would occur either when

sigma is higher than 0.35 or when ReθS is lower than 125. Gaster [30] also prosed a

two parameter criterion but introduced a different pressure parameter P, defined as: P = (θS2/ν)(dU/dx)av. Furthermore, based on a large number of experimental

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1.3. BUBBLE BURSTING 5

in terms of a curve separating short from burst bubbles. Horton [39], rather than just a bursting criterion, developed a model for the whole separation bubble in order to determine the bursting onset conditions. He could make use of extensive experimen-tal results (especially those of Gaster) as well as Stratford’s [80] work dealing with turbulent and laminar boundary layer separation. Based on a steady- time averaged interpretation of Gaster’s results, he identified the bursting process as the breakdown of turbulent reattachment. This is the classical model we outlined above. In Horton’s criterion, bursting is assumed to take place when the theoretical pressure recovery curve does not cross the inviscid pressure distribution. As shown by Horton, this criterion is the same as Crabtree’s criterion (only with the limiting σ equal to .48 in-stead of .35) and is in acceptable agreement with Gaster’s criterion. Successive effort has been devoted to the refinement of Horton method, without however changing the physical idea of the phenomenon. Roberts [67] calibrated Horton’s model by slightly modifying some of the relations he used in the light of new available experimental data. Schmidt [72] further modified the model using data obtained at particularly low values of the Re number in order to improve its accuracy. He concluded that, in this Re number range, the laminar part of the bubble had a much greater impor-tance on the flow development than Horton allowed for (Horton assumed the flow to be stagnant in the laminar region of the bubble). Dini [18] proposed an interesting bubble model based on the same issue. Shum [74] pointed out that an appropriate tuning of Horton’s method parameters still proved to be much easier and time saving than Dini’s approach, particularly for design purposes. This tuning is however time consuming and difficult especially when no previous experimental data are available. Finally, van Ingen [91] proposed a prediction method based on Stratford’s zero skin friction limiting pressure distribution [80]. This method gave good results for the prediction of bursting on a Wortmann airfoil [91].

As explained at the beginning of this section, more recent research focussed on the un-steady characteristics of the bubble, placing the ”classical” view proposed by Horton in a very different context. This point was discussed in section 1.2.1.

1.3.2 Bubble burst vs turbulent separation

At the beginning of this section, we assumed that leading edge stall is caused by the burst of a laminar bubble in the nose region of the airfoil. A different scenario was, however, proposed in the past by Wallis [93]. In his measurements, leading edge stall was observed to be due to separation of the turbulent boundary layer in the nose region of the airfoil downstream of the bubble and not to the burst of the bubble it-self. Van den Berg [86] later provided a theoretical basis to this point of view, stating that most leading edge stalls would indeed be due to turbulent separation in the nose region. Van den Berg analysis was based on the results of theoretical calculations around the nose of symmetrical Joukowski profiles. Observing that for these profiles the quantity κ = (dU/dx)av/(dU/dx)S never exceeded a value of 1.1, he reduced

Gaster’s two parameters criterion to a modification of Owen’s criterion stating that bursting would occur only if ReθS ≤ 140. By comparing the line corresponding to ReθS = 140 to the results of the compilation of Gault [31], he concluded that bubble

burst was unlikely to take place on leading edge stalling sections in the range of op-eration of conventional airfoils.

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leading edge stall in the operation range of conventional airfoils. Two main flaws are in fact present in van den Berg’s analysis that greatly affect the generality of his conclusions: the assumption on the maximum value of κ and the use of Gault’s graph. First, the assumption that κ never exceeds a value of 1.1 is by no means general. It can be easily seen that it is sufficient that this value raises to 1.5 to modify the curve to ReθS = 170 such that, using Gault’s graph, most leading edge stalls would have

to be related to bubble bursting. Such values are perfectly attainable, considering that some of Gaster’s bubbles burst at values of ReθS as high as 232. Furthermore,

a number of experimental investigations exists which clearly relate bursting occur-rence to leading edge stall and exclude alternative scenarios. A few examples are Gault [55], where the chord Re number was as high as 6 millions, van Dyken [88] and Broeren [11]. We can conclude that the bursting phenomenon is strongly dependent on the pressure distribution on the airfoil and that (at least) a two parameter criterion should be used.

The second shortcoming of van den Berg’s analysis is the use of Gault’s graph. Gault tested a limited number of airfoils and his classification into different stall categories was rather arbitrary. Moreover, no multi-element configuration was tested and al-most all tests were done at Re numbers higher than 1 million. All these considera-tions strongly limit the generality of van den Berg’s theoretical approach while most available experimental evidence suggests that bursting is the most likely scenario to be expected. In this context it is surprising that van den Berg’s conclusions are sometimes assumed to be generally valid, without placing them in the right frame of applicability (see for example [1], page 30).

In the present thesis, bubble bursting will be investigated mainly in terms of bubble characteristics and stability. This is partly justified by the above discussion. Further-more, in the experimental analysis of the slotted configuration performed in chapter 2, bubble bursting seemed the most likely cause of stall. Finally, it should also be noted that even in those cases where van den Berg’s conclusions apply, the conditions of the turbulent boundary layer behind the bubble are crucial to the development of stall. This means that a good comprehension of the characteristics of the bubble is essential also in this case.

1.4 Relevance of laminar bubbles to multi-element

configurations

In the aeronautical world, laminar separation bubbles have traditionally been a con-cern for the aerodynamics of sailplanes and of small aircrafts. However, a number of measurements in the 90’s [1] stressed their importance also for commercial transport aircrafts in slow flight, where laminar bubbles strongly affect the flow on high-lift devices. This is especially true for the slats on a multi-element configuration but also on slotted flaps a similar effect can be observed. In chapter 2 the results of the in-vestigation on the stall behavior of a slotted configuration will be shown that stongly support this consideration. This analogy between laminar bubbles on high lift devices

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1.5. OBJECTIVES OF THE THESIS 7

and on sailplanes and small aircraft, is not surprising, noting that a typical value of Re of an order of 106_{based on the chord of the whole configuration can easily become}

a value falling in the range of, for instance, the wing of a sailplane, when based on the chord of the flap or the slat. Furthermore, the boundary layer over a slotted flap tends to stay laminar longer due to the favorable pressure gradient originating from the slot flow, increasing the possibility of bubble formation.

Compared to the single element case, some differences are of course also present, es-pecially in the case of the flap. For instance, the wake of the main airfoil plays an important role both in keeping the boundary layer over the flap attached longer and in influencing the transition process through the contamination mechanism. Wake merging and wake bursting [85] are also important issues. Keeping this in mind, it is, however, clear that an improvement in the prediction of the behavior of the laminar bubble, especially close to stall, would be beneficial also to the design of high lift devices. This point will be further discussed in chapter 2.

1.5 Objectives of the thesis

In spite of all research efforts, many crucial points regarding the structure and be-havior of laminar separation bubbles are still controversial and/or unclear. At the same time, the interest in the behavior of laminar bubbles is rising, because of their importance in many engineering problems. Within the aeronautical community, the discovery of the relevance of laminar bubbles for high lift design further drew atten-tion on the understanding of their characteristics. The main objective of this thesis is to investigate the unsteady characteristics of laminar separation bubbles with the ultimate goal of an improved prediction of bubble behavior during the design pro-cess, especially close to stall conditions. More in detail, the objectives of the present investigation can be summarized as follows:

I Investigate the bubble bursting and stall hysteresis phenomenon on a single slotted flap high-lift configuration in order to define the problem and to identify possible areas of improvement of existing prediction methods.

II Improve the understanding of the physics involved, focussing on:

1. the dynamics and characteristics of the vortical structures present in the bubble and their dependence on Reynolds number and pressure gradient variations.

2. the characteristics of the turbulent boundary layer developing behind the bubble.

3. the relevance of the level and nature of upstream disturbances to the bubble (steady and unsteady) structure.

4. the prediction of the bursting phenomenon.

A side objective will also consist of building up, for the setup of chapter 3, a set of detailed experimental reference data in natural flow conditions useful for further CFD analysis (such as that of chapter 4).

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The pressure measurements on the high-lift configuration clearly defined the bubble bursting and stall hysteresis phenomenon. However, only by comparing these results with the numerical predictions we could identify flaws and possible areas of improve-ment (point I of previous section). To this purpose, both boundary layer and unsteady Navier-Stokes calculations were performed.

More detailed measurements were needed in order to investigate point II of previous section. To this purpose, LDA and PIV optical measurements were carried out on a Gaster like setup. The combined use of these optical techniques allowed to investigate in great detail both the steady and unsteady characteristics of the bubble. However, Navier-Stokes calculations were also needed in order to extend the range of parameters that could be investigated with the experiments. Furthermore, these computations allowed to shed more light on a number of issues related to the stability of the bubble and to the relevance of upstream disturbances.

1.7 Outline of the thesis

Our interest in the behavior of the laminar bubble close to stall was first raised by the experimental results obtained on a slotted multi-element configuration. These results and the successive experimental and numerical analysis of this slotted multi-element configuration will be presented in chapter 2. One of the conclusions of chapter 2 was, however, that a different setup was needed in order to perform a more detailed investigation of the bubble characteristics. For this reason, detailed measurements using the LDA and PIV optical techniques were carried out on a Gaster like setup, focusing on the unsteady structures of the bubbles. The results of this experimental investigation are shown in chapter 3. In order to investigate the relevance of upstream disturbances and the dependance on Re number and pressure gradient, the numerical analysis described in chapter 4 was also carried out on the same setup.

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Chapter 2

Bubble bursting and stall

hysteresis on a single slotted

flap high-lift configuration

The interest in bubble bursting, which, especially on multi-element configurations has not been thoroughly investigated yet, was raised by the experimental results obtained while testing a computer designed flap [83] in the low speed Low Turbulence wind Tunnel facility of the Delft University of Technology [26]. A sudden and dangerous stall was found to occur over the flap surface. The reason for this was the bursting of a laminar bubble in the nose region of the flap which was not predicted by the Boundary Layer code [23] used for the design of the flap. Once bursting occured, an hysteresis loop in the Cl − α curve was observed. This loop is a real danger due to the large ∆α jump which is needed to resume pre-stall conditions.

Present numerical design codes do not help the designer much in predicting this im-portant phenomenon, and wind-tunnel testing remains necessary. Furthermore, the physical mechanism leading to the bursting of the bubble is not fully clear yet. The purpose of the investigation reported in this chapter (also published in [7], [8]) was to shed light on the bursting phenomenon with the ultimate goal of improving ex-isting prediction methods. In this chapter, this was attempted by means of additional experiments and numerical calculations on the complete multi-element configuration (pressure measurements, boundary layer and N-S calculations). When possible, the focus is on the unsteady structures present in the flow, for the reasons explained in section 1.2.1.

After an introductory part dealing with the characteristics of multi-element configu-rations and of stall hysteresis, we will present the experimental evidence followed by the numerical investigation.

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..

nition.

2.1 Introduction: bursting on slotted multi-element

configurations

Slotted multi-element configurations are very effective in raising the maximum lift of airfoils in take-off and landing conditions. However design details are important since slight changes in the geometry and relative position of the elements may have a large influence on stall behavior. The choice of gap and overlap dimensions is especially critical (fig. 2.1). The main focus of high lift design is to maximize the Clmax, while

less attention is devoted to post-stall flow development. This practice can lead to a dangerous optimum design, especially for Reynolds numbers up to an order of 106

when laminar separation bubbles are involved. The bursting of a laminar bubble causes a hysteresis loop in the Cl − α curve that can turn out to be rather large. The result is a very dangerous situation, due to the combination of the sudden lift loss and the large ∆α reduction which is needed to resume pre-stall conditions. This is particularly relevant for the flap of a multi-element configuration where the possible occurrence of such a situation was discovered only recently [9, 26].

The formation of laminar bubbles on the leading edge of a single-element airfoil and their possible bursting are known to strongly affect the stall behavior of single-element airfoils. The possibility of bursting and stall hysteresis, however, is often disregarded during the design process. When experiments are done, it is not uncommon that tests are stopped just after stall occurs, with no interest in post-stall behavior. On the other hand, existing bubble bursting predictors perform badly, especially in the low Re range, unless an accurate and dedicated tuning against available (if any) experiments is performed [74]. The most widespread numerical design codes for single- and multi-element airfoils (for example XFOIL [24], MSES [23] and the Eppler code [28]) lack the required accuracy to predict stall behavior and do not include any of these bursting predictors. The designer currently relies heavily on experimental analysis, much more than for cruise conditions.

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2.2. STALL HYSTERESIS: THEORETICAL BACKGROUND 11

In this chapter, particularly the 2-D physics and airfoil design issues in relation to bubble bursting, will be addressed. The 2-D case permits a much deeper and detailed investigation of the driving flow phenomena [52] than does the 3-D approach and for ordinary unswept wings, 3-D effects are usually limited to a small region near the tip (a definition of the global characteristics of 3-D separation and of its topology is still a matter of discussion [87, 100]). In addition, transition at low Re numbers develops mainly as a 2-D process. All evidence suggests that the amplification of 3-D disturbances by secondary instabilities is in fact less rapid in this case, being somehow ”locked” on a dominant 2-D wave frequency [66].

In the following sections, the experimental and numerical results obtained during and after the design process of a multi-element single slotted flap configuration will be presented. Finally, a number of physical aspects will be addressed that are not included in the classical model of a laminar bubble and hence not accounted for in the existing bursting prediction methods, indicating a possible direction for improvement. These results show that the bubble present in the nose region of the flap of this slotted configuration was extremely important in determining the performance of the whole multi-element configuration. When this bubble bursted and the flap stalled, a sudden loss of lift and a large hysteresis loop followed, a behavior similar to that observed in the single-element case. This is an important and rather new finding [9, 10] as the possibility of bursting and stall hysteresis is usually ignored in the process of designing a new flap. The Reynolds number range where this bursting may happen is found to be higher than for single-element airfoils. The experiments presented in this chapter were carried out at a Reynolds number (based on the chord of the main element) of about 2 million, as required by the specifications of the EAGLET two-seater training motor plane for which the flap had been designed. This value of 2 million is a typical value for general aviation airplanes in landing conditions. It may hence be expected that the findings for the current setup should have a more general significance and that the possibility of bursting should be regarded as a major danger during the design of a flap for low Reynolds number applications.

2.2 Stall hysteresis: theoretical background

2.2.1 Stall hysteresis on a single-element airfoil

Once bubble bursting occurs, a hysteresis loop in the Cl − α curve is observed. When it is present, this loop represents a real danger for pilots. The main reason why uncovering the physics behind the bursting of a laminar bubble is such an important issue is indeed to be able to prevent stall hysteresis occurrence.

A review of hysteresis can be found in Biber [9] both for fixed and rotary wings. Here the concern is particularly with fixed wing aircrafts, where the phenomenon is usually referred to as stall hysteresis. A short description of a typical hysteresis loop may be given as follows. By raising α, the laminar bubble first moves towards the leading edge diminishing its length. Suddenly it bursts turning into a completely separated flow or into a long bubble which widens towards the trailing edge of the profile until ultimately the flow is completely separated. If at this stage α is decreased, the flow will remain separated for a while before the bubble is again formed thus giving raise to the observed loop in the Cl−α curve. It should be noticed that at low Re almost every

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if the curvature of the nose is high enough. In many cases, including the NASA experiments on which Gault’s work was based, the hysteresis is then not detected because in the experiments the angle of attack was not reduced after bubble bursting.

2.2.2 The slotted multi-element configuration

The idea to split an airfoil in more elements dates back to the end of World War I when a German engineer-pilot, G.V. Lachmann (who had just survived a crash following a stall during its early training flights) first proposed it to Prandtl. The results of the ensuing experimental tests were indeed encouraging, with spectacular lift increase beyond 30% of the basic value, in some cases, demonstrating the validity of the proposal. The principle on which it works has been, however, misinterpreted for many years after these early applications. It became more and more clear that the slot does not work as a boundary layer control device but, as Smith [76] pointed out, owes its remarkable performance mainly to the change it produces in the characteristics of the external inviscid flow. The pressure rise over the whole configuration is split into a number of less severe pressure rises, thus leading to the large overall lift increase observed in the experiments. Both the circulation around the main airfoil and the effect of its wake act in the direction of reducing the pressure peak in the nose region of the flap which can then delay separation and in turn raise the circulation and the lift contribution of the main element. Another important feature is that at each element a new boundary layer develops. However, when large separated regions, usually on the flap surface, are present, viscous effects become decisive and they put an upper limit to the achievable lift increase.

2.2.3 Stall hysteresis on a slotted multi-element configuration

While it is a well known and identified flow feature in the case of single-element air-foils, the possibility of stall hysteresis over multi-element configurations seems to be poorly known and there is little in the literature about the subject.

Like for the single-element case, bubble bursting and stall hysteresis are readily con-nected. The flow on the flap behaves in a very similar way displaying after bursting a typical leading edge stall pattern. In the slotted multi-element case, the main el-ement wake and the direction and the strength of the slot flow are very important additional factors that are absent in the single-element case. They strongly affect the flow development on the flap and the possible burst of the bubble in its nose region. Due to the reduced pressure gradient, the boundary layer over the flap tends to stay laminar longer, provided that turbulence contamination from the main airfoil wake is avoided. In addition, the chord of the flap is much shorter than the main airfoil, so that a scale effect on the Re number is present. In our case an upstream Re = 2 · 106

becomes a Re = 436000 when based on the 21.8%C chord of the flap, clearly falling in the range where stall hysteresis is more likely to occur on single-element airfoils. This effect is much stronger once the gap (fig. 2.1) is made wider, since the flow around the flap becomes less dependent on the flow over the main element. When bubble

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2.3. DIFFICULTIES IN CURRENT HIGH LIFT DESIGN PRACTICE 13

bursting occurs on the flap, the pressure distribution over the flap surface suddenly collapses. The reduced circulation of the flap reduces in turn the circulation of the main element leading to a global effect on the flow over the entire airfoil system. Here again, the angle of attack must be lowered considerably before the flap reaches again pre-stall conditions, giving rise to the observed hysteresis loop. Hence, the bursting on the flap controls the hysteresis on a multi-element airfoil.

2.3 Difficulties in current high lift design practice

2.3.1 Numerical modelling difficulties

Both stall and post-stall behavior should be taken into account in order to achieve an optimum high lift design. For a prediction of post-stall evolution, a Navier-Stokes code or at least a dedicated treatment of the separated region would be required [14]. The use of a Navier-Stokes code, however, is usually not an option for high lift design purposes. There are two main reasons for this. The first one is more general and is valid also when laminar bubbles are absent, i.e. the large computational time involved and the high number of parameter combinations that should be tested. The second is that the physics of bursting and the mechanism of transition, especially close to or after bursting, are not clear yet and so no reliable model is available. An unsteady DNS solver would then be required. This option is currently not viable, not only for design purposes.

As a numerical tool for 2-D high lift design, boundary layer codes are at present the usual choice, for both single-element airfoils and for multi-element high-lift configu-rations. Although some of these codes can deal even with large separated regions, the results are not as satisfactory as for attached flows [6], ultimately leading to the breakdown of the code when the separated region becomes too extensive. Hence, for the problem analyzed here, not more than a warning on bubble bursting occurrence can be expected. However, an accurate prediction of the onset of bursting is very important because parameter changes leading to Clmaximprovement are also driving

bubble bursting occurrence and because of the strong link between bursting and the hysteresis phenomenon.

Many semi-empirical methods to predict bursting onset have been proposed in the past (see, for instance Crabtree [16], Horton [39], van Ingen [90], Dini [18], Shum [74]). All of them, however, do not successfully predict bubble bursting in all flow conditions and especially in the low Re range, where they require a very accurate tuning to work well. This tuning is time consuming and extremely difficult when no previous exper-imental data are available. For this reason these methods are not practical and most boundary layer codes for design purposes do not include them. In addition, these codes usually show no sign of breakdown when close to the conditions when bursting occurs in the experiments. As a result of these modelling difficulties, experimental tests are necessary in order to verify the numerical design.

2.3.2 The flap of the EAGLET

In the present investigation, one of the most widespread and efficient boundary layer design codes, the MSES code developed by Drela [23], was used for the design of a

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the cruise configuration was found satisfactory, but when testing the landing config-uration (30 degrees flap deflection and Re = 2 · 106_{), large discrepancies with the}

numerical predictions were found. In the next sections, first the experimental results will be shown. The computational results are shown next.

2.4 Experimental investigation

2.4.1 Experimental setup

The LTT of the Delft University of Technology is a closed return type wind tunnel with a contraction ratio of 17.9, see [19] and [26]. The test section is 1.8 meters wide, 1.25 meters high and 2.6 meters long. The tunnel is designed for a maximum speed in the test section of 120 m/s. The turbulence level is low and varies from 0.018% at 10 m/s up to 0.1% at 100 m/s. To prevent separation at wing-wall junctions, suction boxes were attached to the test section wall during this investigation. The amount of suction was chosen according to Foster [29] and the resulting flow behavior was checked through tufts applied near the trailing edge of the flap and main element surfaces.

The composite wind tunnel model has a flap nested chord of .6 meters and a span of 1.25 meters. The flap chord is 21.8% of the total chord with flap nested. The model was installed vertically in the test section and equipped with 59 pressure orifices on the main wing and 23 on the flap (.4 mm diameter) located in diagonal rows between .45 meters and .55 meters from the top of the test section. The surface of the model consists of polyester gelcoat which has been polished to ensure an aerodynamically smooth finish.

A total and static pressure wake rake, mounted on a cross beam, was positioned be-hind the model, with the tips of the total pressure tubes at 57% of the total chord downstream of the flap trailing edge. A pitot static tube was mounted on the side wall in front of the model, at about two chord lengths from the leading edge. All pressure taps were connected to a multi-tube liquid manometer (200 tubes) equipped with an automatic optical reading device.

The measured pressure coefficients were numerically integrated (trapezoidal rule) to obtain the main element and flap normal force and pitching moment coefficients. The section profile drag coefficient was computed from the wake rake total and static pres-sures using Jones method [45]. Standard low speed wind tunnel boundary corrections have been applied to the data according to the method of Allen [5].

2.4.2 Experimental accuracy

The automatic reading device reads the manometer tubes with an accuracy of 0.1 mm, about 1 Pa. Due to the need of a reference run, the accuracy in the measured pressure values is therefore of 2 Pa. A specially developed speed control system is installed in the wind tunnel, accurate within 0.02% of the set speed. Taking into account these values, the uncertainty UCp of the measured Cp due to inaccuracies in

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2.4. EXPERIMENTAL INVESTIGATION 15

..

Figure 2.2: Observed relationship between gap-overlap and hysteresis occurrence in the measured range (from α ∼ −6 degrees to α ∼ 16 degrees). Re = 2 · 106_{, NACA}

63-415 airfoil with slotted flap.

the manometer and in the speed control can be estimated [48]. Other inaccuracies are of course also present, for example those due to defects and size of the pressure holes. Only the uncertainty due to inaccuracies in the manometer and in the speed control is, however, considered in the following estimate. Focusing on the 3.0% gap 1.0% overlap arrangement, we estimate a value of UCp = ±0.0018 at 0 degrees and

a value of UCp = ±0.0043 at 10 degrees. These are roughly the largest and smallest

uncertainties for the 3.0% gap 1.0% overlap arrangement. The uncertainties stay of the same order of magnitude for the other arrangements as well. The uncertainty Uα

in the angle of attack is Uα= ±0.01 degrees. The uncertainty in the gap and overlap

measurements, Ug,o, is estimated to be about 0.1 mm, hence 0.02% of the chord

(Ug,o = ±0.02%). The uncertainty in the integrated quantities is more difficult to

estimate. It depends on the spacing between the orifices and it is higher in the regions of high pressure gradients (i.e. close to the nose). Errors due to three-dimensionality of the flow were minimized by the suction applied at the wing-wall junctions.

2.4.3 Experimental results

All pressure distributions presented in this section are measured with a gap of 3% and an overlap of 1% of the chord. However, lift and drag curves from other flap settings are also presented to show the trends resulting from changes in gap-overlap. All results shown are relative to the flap in landing configuration (30 degrees deflection). A scheme relating the gap-overlap settings to the occurrence of the hysteresis loop is shown in fig. 2.2. The effect of a change in gap dimension was particularly investigated. For the overlap, only two different setups were checked, 1% and 2%. As can be seen in

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Figure 2.3: Effect of gap variation before bursting occurrence (overlap 2.0%). Re = 2 · 106_{, NACA 63-415 airfoil with slotted flap.}

fig. 2.2, a raise in the gap increases the possibility of a hysteresis loop. For a gap value of 1.5% no hysteresis was observed. On the other hand, for a gap value of 4%, the flow over the flap was always separated at all measured angles of attack. Changes in the overlap value around the computed optimum position seemed to be less relevant to the occurrence of hysteresis than a change in the gap. However, for 2.0% gap, hysteresis was observed for an overlap value of 1%, but not for an overlap of 2%. For a 1% overlap and 2.5%, 3.0% gap values, the flap was separated at the beginning of the measurements (α = 0) and α had to be lowered first, before obtaining an attached flow on the flap surface. This effect is rather peculiar and is reported also by Biber [9]. When bubble bursting does not occur, a wider gap enhances the performance of the configuration in terms of lift coefficient. This effect can be seen clearly in fig. 2.3, where the Cl − Cd polar and the lift curve for 1.5%, 2.0% and 2.5% gap, with 2.0% overlap are shown. The maximum Cl increases by increasing the gap, ranging from Clmax= 2.4 to Clmax = 2.5 up to Clmax= 2.52 respectively. However, a wider gap

increases also the danger of bubble bursting over the flap surface as can be seen in fig. 2.4, where the Cl − Cd polar and the lift curve for 3.0%, 3.5% and 4% gap, with 2.0% overlap are shown. The maximum Cl drops from a value of Clmax = 2.53 for

gap 3.0% to Clmax= 1.9 for 3.5% and 4% gap. This represents a quite critical issue

when designing a flap because the gap is easily made too wide if bubble bursting is not taken into account properly. The hysteresis loop for 3.5% gap is also shown in fig. 2.4.

The 3% gap and 1% overlap case was chosen for detailed investigation of stall hysteresis and comparison with the numerical analysis. The large clockwise hysteresis loop that occurred in this case can be clearly seen from the Cl − Cd and Cl − α curves

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2.4. EXPERIMENTAL INVESTIGATION 17

Figure 2.4: Experimental drag and lift coefficient for gap 3.0%, 3.5% and 4% (overlap 2.0%) showing the hysteresis loop for the 3.5% case. Re = 2 · 106_{, NACA 63-415}

airfoil with slotted flap.

shown in fig. 2.5 (the numerical results will be discussed in the next sections). The corresponding pressure distributions are shown in fig. 2.6 for several angles of attack covering the entire hysteresis loop. At the beginning of this test (α = 0), right after turning on the wind tunnel, the flow over the flap was completely separated. The flow attached only after α had been lowered to -6 degrees (fig. 2.6(a)). Starting from this value, the pressure distributions on the flap and main airfoil were recorded. Raising α from -6 degrees up to 11 degrees (fig. 2.6(a)- 2.6(f)), the flow on the flap stayed attached. The main airfoil kept on gaining lift, while the pressure peak on the flap nose slightly reduced as α was increased. From fig. 2.5(b) it can be seen that the Cl of the whole configuration increased up to a maximum of about Clmax = 2.6

for α = 11 degrees. At α = 11.5, however, the pressure distribution over the flap suddenly leveled, as can be seen in fig. 2.6(i). As a result, the Cl dropped to a value of about Clmax = 1.9 (fig. 2.5(b)) while the Cd increased to almost twice its value

before bursting (fig. 2.5(a)). The angle of attack was still raised up to 15 degrees (fig 2.6(j)). The trailing edge separation on the main element, that could hardly be noticed in fig. 2.6(f) and fig. 2.6(i), is now covering most of the main element surface, resulting in a further loss of Cl and increase of Cd (fig. 2.5). When lowering the angle of attack, the flow on the flap stayed separated far beyond the value of α = 11.5 degrees where bursting first occurred (fig. 2.6(k)- 2.6(m)), causing the hysteresis loop of fig. 2.5(b). The angle of attack had to be lowered down to -6 degrees to obtain again an attached flow on the flap, see fig. 2.6(n).

The reason for the hysteresis occurrence is thus in this case readily identified with the flap flow behavior. The pressure distributions show that the flow over the flap

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main airfoil has been reported on other multi-element configurations [9] and appears after bursting also in the present analysis, as can be seen from the pressure distribution at 15 degrees. At bursting however (for α between 11 and 11.5 degrees), while the pressure over the flap is leveled, only the effect due to the loss of circulation is evident on the main wing. The flow appears to be separated close to the trailing edge of the main element but this seems in this case to be the consequence rather than the cause of the separation on the flap.

Figure 2.5: Gap 3%, overlap 1%: experimental results and computational predictions. See also fig 2.6. Re = 2 · 106_{, NACA 63-415 airfoil with slotted flap.}

2.5 Computational investigation (design code)

The MSES code solves the Euler equations strongly coupled to a two-equations in-tegral boundary layer formulation. Two-point central differencing is generally used to discretize the boundary layer equations. A transition prediction method of the en _{type [92] is included in the viscous formulation. The complete set of equations is}

then solved by a global Newton method so that strong viscous-inviscid interactions can be taken into account [23]. MSES has proven to be a very useful tool for multi-component airfoil design purposes. It is currently widely used for the design of many successful airfoils. Large separation regions can, in principle, be handled, although, as for all other boundary layer codes [6], the results are less accurate. The code is a steady solver and thus unsteady effects cannot be captured. As for all other codes for design purposes, MSES does not include any bursting criterion and no warning regarding its possible onset is given to the designer.

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2.5. COMPUTATIONAL INVESTIGATION (DESIGN CODE) 19

..

(a) α = −6 deg., beginning of the measures.

.. (b) α = −2 deg., raising. .. (c) α = 2 deg., raising. .. (d) α = 4 deg., raising. ..

(e) α = 8 deg., raising.

..

(f) α = 11 deg., raising.

Figure 2.6: Hysteresis loop for gap 3% ov. 1%: pressure distribution. Re = 2 · 106_,

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..

(i) α = 11.5 deg., raising: bursting on the flap.

..

(j) α = 15 deg., maximum α reached in the exper-iment. .. (k) α = 10 deg., decreasing. .. (l) α = 6 deg., decreasing. .. (m) α = 2 deg., decreasing. ..

(n) α = −6 deg., decreasing: pressure recovery on the flap.

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2.5. COMPUTATIONAL INVESTIGATION (DESIGN CODE) 21

(a) lower branch of the hysteresis loop (b) upper branch of the hysteresis loop Figure 2.7: Pressure distribution on the flap for α = 8 degrees, 3% gap and 1% overlap: experimental results vs computational predictions. Full lines are calculations. Re = 2 · 106_{, NACA 63-415 airfoil with slotted flap.}

2.5.1 Numerical accuracy

A convergence study in space was performed using three different grids with a refine-ment ratio of√2 comparing the values of the Cl and Cd of the whole configuration (the grids had about 2, 4 and 8 thousands points with respectively 64, 92 and 132 points on the flap surface and 94, 136 and 188 on the main element). Following Stern [79] it is then possible to check under which convergence condition the calculations are performed. This can be done by looking at the ratio R between the solution changes for medium-fine and coarse-medium solutions. In this case, a value of R = .1546 was found which means a monotonic convergence condition which allows an estimate for the order of accuracy and the leading order term of the space discretization error of the solution. For this, generalized Richardson-extrapolation is used [79] giving an order of accuracy of 5.4 against an expected theoretical value of 2. This result for the order of accuracy means that the solutions are not in the asymptotic range and that the leading order term of the series expansion estimating the error, underpredicts the error. The uncertainty UCl, i. e. an estimate of the error on the Cl value, will thus be

estimated [79]. Using a correction factor accounting for the higher order terms [79], a value of UCl = ±0.0198 is found. Performing a similar analysis for the Cd values,

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7 was chosen based on previous experience with the design and wind-tunnel testing of the wing airfoil for the general aviation aircraft EXTRA 400 [83]. The grid used was the most refined used in the accuracy analysis (197x40 points).

The case with 3.0% gap and 1.0% overlap will be especially compared with the experi-mental findings. From fig. 2.7, it is interesting to notice that the pressure distribution over the flap as computed appears to be physically different from the experimental re-sults. The computed model predicts a small laminar bubble at about 20% of the flap chord followed by a turbulent separation which approaches the reattachment point of the bubble when α is increased. This result is very different from the sudden leading edge stall observed in the experiments. No relevant turbulent separation previous to bursting is evident from the experimental pressure plots on the flap. Figures 2.8 and 2.9 show a typical skin friction coefficient and boundary layer parameters (δ∗

and θ) distribution as given by MSES in this situation. On the upper surface, the skin friction becomes zero at the location of laminar separation X/C = .857 and it stays negative over the length of the bubble before being zero again at turbulent reattachment, X/C = .868. After turbulent reattachment it becomes zero again at about X/C = .92, being the location of the predicted turbulent separation. Looking at fig. 2.9, both θ and δ∗ _{display a large increase after turbulent separation before}

decreasing in the wake. The stall behavior on the flap is controlled by the turbulent separation proceeding from the trailing edge, with transition taking place in the bub-ble just before the reattachment point. The experiments show, however, that stall suddenly takes place on the flap as a result of bursting of the laminar bubble, with no previous relevant separation taking place on the flap surface. Consequently, MSES underpredicts the lift and overpredicts the drag. To show this, the computed Cl − Cd polar and Cl − α curves for 3.0% gap, 1% overlap are compared with the measured ones in fig. 2.5. The large separated region after turbulent separation predicted by the code, is responsible for these discrepancies. The presence of unsteady structures in the flow, which is of course not modeled in the code, may well be one of the reasons for this result (see section 1.2.1 and the rest of this chapter).

2.6 Computational investigation (N-S code)

To investigate the relevance of unsteady structures to the present flow field, Navier-Stokes calculations, both laminar and RANS, were first performed on a single-element configuration, namely the Eppler E387 airfoil (Re = 105_{) and then on the}

multi-element configuration tested in the wind tunnel (Re = 2 · 106_{). The results show that}

a strong vortex shedding can potentially originate from the separated shear layer, both on the flap and on the single-element airfoil, suggesting a close connection be-tween the two cases. The effect of transition on the structure of the bubble was also investigated by imposing and then varying the transition point. The computational results suggest that the unsteady behavior of the laminar bubble has to be regarded as a major issue in order to find an effective bursting predictor method for airfoil design.

Unsteady Characteristics of Laminar Separation Bubbles; An Experimental and Numerical Investigation

UNSTEADY CHARACTERISTICS OF LAMINAR SEPARATION

BUBBLES

UNSTEADY CHARACTERISTICS OF LAMINAR SEPARATION

BUBBLES

Summary

Samenvatting

Contents

Chapter 1

Introduction

1.1

Laminar separation bubbles

1.2

Early studies on laminar separation bubbles

1.2.1

The unsteady structure of the bubble

1.3.1

Bubble bursting predictors

1.3.2

Bubble burst vs turbulent separation

1.4

Relevance of laminar bubbles to multi-element

configurations

1.5

Objectives of the thesis

1.7

Outline of the thesis

Chapter 2

Bubble bursting and stall

hysteresis on a single slotted

flap high-lift configuration

2.1

Introduction: bursting on slotted multi-element

configurations

2.2

Stall hysteresis: theoretical background

2.2.1

Stall hysteresis on a single-element airfoil

2.2.2

The slotted multi-element configuration

2.2.3

Stall hysteresis on a slotted multi-element configuration

2.3

Difficulties in current high lift design practice

2.3.1

Numerical modelling difficulties

2.3.2

The flap of the EAGLET

2.4

Experimental investigation

2.4.1

Experimental setup

2.4.2

Experimental accuracy

2.4.3

Experimental results

2.5

Computational investigation (design code)

2.5.1

Numerical accuracy

2.6

Computational investigation (N-S code)