Increasingly stringent emissions regulations have led combustion system designers to look for more environmentally combustion strategies. For gas turbine combustion, one promising technology is lean premixed combustion, which results in lower flame temperatures and therefore the possibility of significantly reduced nitric oxide emissions. While lean premixed combustion offers reduced environmental impacts, it has been observed to experience increased possibility of the occurrence of combustion instabilities, which may damage hardware and reduce efficiency. Thermoacoustic combustion instabilities occur when oscillations in the combustor acoustics and oscillations in the flame heat release rate form a closed feedback loop, through one of two possible mechanisms. The first is direct coupling which occurs due to the mean mass flow oscillations induced by the acoustic velocity. Secondly, the acoustics may couple with the flame due to acoustic interactions with fuel/air mixing, resulting in an oscillating equivalence ratio. Only velocity coupling was considered in this study. The methodology used in this study is analysis of instabilities through linear systems theory, requiring knowledge of the individual transfer functions making up the closed-loop system. Methods already exist by which combustor acoustics may be found. However, significant gaps still remain in knowledge of the nature of flame dynamics. Prior knowledge in literature about the flame transfer function suggests that the flame behaves as a low-pass filter, with cutoff frequency on the order of hundreds of hertz. Nondimensionalization of the frequency by flame length scales has been observed to result in a convenient scaling for the flame transfer function, suggesting that the flame dynamics may be dominated by spatial effects. This work was proposed in two parts to extend and apply the body of knowledge on flame dynamics. The phase one goal of this study was to further understand this relationship between the flame heat release rate dynamics and the dynamics of the reaction zone size. The second goal of this work was to apply this flame transfer function knowledge to predictions of instability, validated against measurements in an unstable combustor. Both of these goals meet an existing practical need, providing a design tool for prediction of potential thermoacoustic instabilities in a combustor at the design stage.Measurements of the flame transfer function were made in a swirl-stabilized, lean-premixed combustor. The novel portion of these measurements was the inclusion of spatial resolution of the heat release rate dynamics. By using a speaker, a sine dwell excitation to the velocity was introduced over the range of 10-400Hz. Measurements were then made of the input (inlet velocity) and output (heat release rate, or flame size) resulting in the flame transfer function. The spatial dynamics measurement was approached through several measures of the flame size: the volume and offset distance to the center of the heat release. Each was obtained from deconvoluted, phase averaged images of the flame, referenced to the speaker excitation signal. The results of these measurements showed that the spatial dynamics for each of these three measures were virtually identical to the heat release rate dynamics. This suggests a quite important result, namely that the flame heat release rate dynamics are completely determined by the dynamics of the flame structure. Therefore, prediction of flow structure interaction with the flame distribution is crucial to predict the dynamics of the flame. These spatially resolved transfer function measurements were used in conjunction with the linear closed-loop model to make predictions of instability. These predictions were made by applying the Bode stability criterion to the open-loop system transfer function. This criterion states that instabilities may occur at frequencies where the heat release rate and acoustic oscillations occur in phase and the system gain has a value greater than unity. Performing this analysis on the combined system transfer function yielded results that agreed quite well with actual instability measurements made in the combustor. Closed-loop predictions identified two possible modes for instability, both of which were observed experimentally. One mode resulted from an acoustic peak around 160 Hz, and occurred at lean equivalence ratios. A second mode occurred at lower frequencies (100-150 Hz) and was associated with the increase in flame transfer function gain at increasing equivalence ratios. These are some of the first successful predictions of combustion instability based on linear systems theory. When multiple modes were predicted, it was assumed that if non-linear effects were to be considered, the lower frequency mode would become the dominant mode at these operating conditions due to its higher gain margin. Also of note is that in the practical system, high frequency oscillations are observed, but not predicted, associated with harmonics of the low frequency mode due to the linear nature of the predictions. While these non-linear effects are not captured, the linear predictive capability is thought to be most important, as from a practical perspective, instabilities should be avoided altogether. The primary findings of this study have significant applications to modeling and prediction of combustion dynamics. The classic heat release rate flame transfer function was observed to coincide almost exactly with the flame size transfer functions. The time scales observed in these transfer functions correspond to convective length scales in the combustor, suggesting a fluid mechanical basis of the heat release rate response. Additionally, linear systems theory predictions of instability based on the measured flame transfer functions were proved capable of capturing the stability of the actual combustor with a reasonable degree of accuracy. These predictions should have considerable application to design level avoidance of combustion instability in practical systems. / Ph. D.

Η παρούσα διδακτορική διατριβή με τίτλο «Αλληλεπίδραση Ομόρροπα Περιστρεφόμενων Στροβίλων Απορρέματος» αφορά την πειραματική μελέτη του ροϊκού πεδίου της αλληλεπίδρασης δύο ομόρροπα περιστρεφόμενων στροβίλων που δημιουργούνται από επιφάνειες άντωσης. Η μελέτη αυτού του φαινομένου έχει καταστεί ιδιαίτερα σημαντική κυρίως τις τελευταίες δεκαετίες, με αφορμή ατυχήματα αεροσκαφών τα οποία αποδόθηκαν στη δράση του στροβίλου απορρέματος. Η διερεύνηση του μηχανισμού αλληλεπίδρασης και συγχώνευσης του συστήματος δύο στροβίλων έχει αποτελέσει αντικείμενο ενδιαφέροντος για πολλούς ερευνητές σε όλο τον κόσμο. Παρόλα αυτά, ακόμη και σήμερα η γνώση και κατανόηση τέτοιων προβλημάτων δεν ανταποκρίνεται στις σύγχρονες απαιτήσεις. Η ερευνητική δουλεία που έχει γίνει έχει σαν στόχο να συμβάλει στην εξέλιξη της επιστημονικής γνώσης γύρω από το πολύ σημαντικό πρόβλημα του στροβίλου απορρέματος. Η ερευνητική εργασία είναι πειραματική και περιλαμβάνει μετρήσεις του ροϊκού πεδίου πίσω από διαφορική πτέρυγα, τύπου NACA 0030, τοποθετημένη σε ροή αεροσήραγγας ανοικτού κυκλώματος. Σκοπός της μελέτης αυτής είναι η διερεύνηση της δομής και δυναμικής εξέλιξης του τρισδιάστατου πεδίου ταχύτητας-στροβιλότητας του παραγόμενου ζεύγους ομόρροπα περιστρεφόμενων στροβίλων κατά τη διάρκεια της αλληλεπίδρασης τους και της φυσικής διαδικασίας συγχώνευσης που ακολουθεί ως τον τελικό σχηματισμό ενός γραμμικού στροβίλου. Η τεχνική μέτρησης που χρησιμοποιήθηκε είναι η "Ανεμομετρία Θερμού Σύρματος" υπό σταθερή θερμοκρασία (constant temperature hot wire anemometry) με χρήση αισθητήρων δύο (X-probe), τεσσάρων και δώδεκα συρμάτων (multi sensors). Η παρούσα πειραματική μελέτη, στην οποία για πρώτη φορά μετρούνται ταυτόχρονα τα μέσα και στατιστικά χαρακτηριστικά των τρισδιάστατων πεδίων ταχύτητας-στροβιλότητας σε ροή αυτού του τύπου, επιχειρεί να καλύψει ορισμένα από τα επιστημονικά κενά που υπάρχουν. Το ροϊκό πεδίο αξίζει την ιδιαίτερη προσοχή, δεδομένου ότι σημαντικοί ανταγωνιστικοί μηχανισμοί εμφανίζονται να επιβάλλουν το δομικό σχηματισμό του πεδίου του ζεύγους στροβίλων και της δυναμικής διαμήκους εξέλιξής του, συμπεριλαμβανομένης και της "διάρκειας ζωής" τους. Το συγκεκριμένο σχήμα έχει σημαντικό ενδιαφέρον επίσης από άποψη εφαρμογών, με δεδομένη την επιδίωξη της μείωσης της επικινδυνότητας του στροβίλου απορρέματος, καθώς οι ομόρροπα περιστρεφόμενοι στρόβιλοι σχηματίζονται, μερικές φορές πολύ κοντά και σε άλλες θέσεις, εκτός από το άκρο πτέρυγας, όπως για παράδειγμα από τα flaps και την άτρακτο και γενικά από όλες τις επιφάνειες άντωσης του αεροσκάφους. / Experimental evidence is reported regarding the structure of the three-dimensional mean and fluctuating velocity and vorticity fields of a turbulent corotating vortex pair. The presented results constitute part of ongoing research on vortex wakes aiming at contributing to the understanding of trailing vortex interaction dynamics and turbulence structure. The flow field under study is the result of interaction of the pair of co-rotating tip vortices formed by a split wing configuration, consisting of two half wings of equal length l = 24.5cm arranged at equal and opposite angles of attack,  =  8 degrees. The airfoil profile of the wings is that of a NACA0030 with cord length c = 10cm. The wing arrangement is placed at the entrance of the test section of a low turbulence subsonic wind tunnel, of dimensions 30cm  50cm  300cm. In the near wake region, simultaneous measurements of the three-dimensional vector fields of velocity and vorticity in the corotating vortex pair were conducted using an in-house designed and constructed 12-hotwire sensors vorticity probe. The probe consists of three closely separated orthogonal 4–wire velocity sensor arrays, measuring simultaneously the three–dimensional velocity vector at three closely spaced locations on a cross plane of the flow field. This configuration makes possible the estimation of spatial velocity derivatives by means of a forward difference scheme of first order accuracy. The probe was calibrated in-situ in the core region of a round jet rotatable about the pitch and yaw directions. Based on preliminary visualization experiments the cross plane at x/c=0.3 (near wake) has been selected as representative of the vortex pair formation. The evolution of the vortex pair interaction (far wake region) was recorded by a 4-hotwire sensor, capable of measuring simultaneously the three-dimensional velocity vector of the flow filed. After shedding the two vortices are swept along the streamwise direction. The cores initially move away from each other. The rotational velocity field around each core induces a rotational velocity to the other vortex and thus both vortex cores are spiraling around each other, developing a braid of two vortices and deforming the external flow field in the downstream direction. Gradually the interaction flow field links both vortices together until the final merging and the formation of a new stable linear vortex. In the near wake location, the flow field is dictated by the pressure distribution established by the flow around the wings, mobilizing large masses of air and leading to the roll up of fluid sheets. Fluid streams penetrating between the wings collide, creating on the cross plane flow a stagnation point and an ΄΄impermeable΄΄ line joining the two vortex centres. Along this line fluid is directed towards the two vortices, expanding their cores and increasing their separation distance. This feeding process generates a dipole of opposite sign streamwise mean vorticity within each vortex. The rotational flow within the vortices obligates an adverse streamwise pressure gradient leading to a significant streamwise velocity deficit characterizing the vortices. As vortices start to interact, the two cores lose their symmetry and obtain an elliptical formation. The corotating vortex pair is observed to merge at about 0.6 orbit periods and at a downstream distance of 7c from wing tips. Visualization experiments show that the instantaneous flow field of the vortices preserves at all times the structural characteristics of the mean flow field. The vortices are continuously formed close to the wing tips and the fluctuating flow field is the result of changes in the intensity of the formation (e.g. larger or smaller vortex core size) or changes in the position of the cores (wandering) which both should be attributed to secondary attenuating flow instabilities. In this sense the relation of the turbulent field to the mean field is significantly different from cases with no identifiable coherent flow structures (e.g. grid turbulence) or flow fields in which the successive presence of distinct structures result in an idealized but never present mean flow structure.

No description available.

Flow separation and reattachment happens in many fluid mechanical situations occurring in engineering applications as well as in nature. The flow over a backward-facing step represents a geometrically simple flow situation exhibiting both flow separation and reattachment. Broadly speaking there are only two important parameters in the problem, the Reynolds number(Re) based on the step height(h),and a geometrical parameter, referred to as the Expansion ratio(ER), defined as the downstream channel height to the upstream channel height. In spite of the relative simplicity of this geometry, the flow downstream is quite complex. The main focus of the present work is to elucidate the unsteady three-dimensional coherent structures present in this flow at large Re, Re>36,000,based on the step height(h). For this, we use velocity field measurements from Particle Image Velocimetry (PIV)in conjunction with hotwire anemometry measurements. The time-averaged structure of this flow is first studied in detail, including the effect of Reynolds number(Re) and Expansion Ratio(ER), on it. These studies show that at sufficiently large Re (Re>20,000), the reattachment length becomes independent of Re. The detailed internal structure of the separation bubble is also found to be independent of Re, but for Revalues that are relatively larger(Re>36,000). At large Re, the main effect of ER ,is found to be on the reattachment length, which increases with ER and saturates for ER values greater than about 1.8. The detailed internal structure of the separation bubble has been mapped at high Re and is found to be nearly the same for all ER, when the streamwise length is normalized by the reattachment length. In order to elucidate the unsteady coherent vortical structures, PIV measurements are done in two orthogonal planes downstream of the backward-facing step. These measurements are done for ER= 1.50 at large Re(Re=36,000) and in a large aspect ratio facility(AR= span length/step height= 24); the latter being important to avoid any effects due to span-wise confinement. In the spanwise plane parallel to the lower wall(x-z plane),instantaneous velocity fields show counter rotating vortex pairs, which is a signature of the three-dimensional vortical structures in this plane. Using conditional averaging, this counter-rotating vortex pair signature is captured right from upstream of the step, to well after reattachment. Spatial correlations are used to get the length scale of these coherent vortical structures, which varies substantially from the attached boundary layer before separation to the region after reattachment. The variation of these structures in the cross-stream (vertical) direction at reattachment and beyond gives an idea about their three dimensional shape. The circulation of these counter-rotating pairs is measured from the conditionally aver-aged fields, and is found to increase with streamwise distance reaching normalized circulation values (Γ/Uoh) of about 0.5 around reattachment. Velocity spectra downstream of the step show peaks corresponding to both the shear layer frequency(Stsl)and a relatively lower frequency that corresponds to large-scale shedding from the separation bubble (Stb); the latter in particular being quasi-periodic. Small amplitude sinusoidal forcing at the shedding frequency(Stb) is applied close to the step, by blowing and suction, to make the quasi-periodic shedding more regular. Measurements show that this has a very small effect on both the mean separation bubble and on the counter-rotating structures in the x-z plane. This mild forcing however enables phase locked PIV measurements to be made which shows the bubble shedding phenomenon in the cross-stream plane(side view or x-y plane). The phase-averaged velocity fields show significant variations from phase to phase. Although there is some hint of structures being shed, from these phase-averaged fields, it is not very clear. One of the primary reasons is the fact that the flow is effectively spanwise averaged, as the three-dimensional structures are not locked in the spanwise direction. To get a three dimensional view of the sheddin gphenomenon, it is necessary to lock the spanwise location with respect to the three-dimensional vortical structures before averaging across the different phases. We use the condition, u’<- urms, to locate the central plane between the counter-rotating structures, which in effect are the “legs” of the three-dimensional structure. With this condition, we effectively get a slice of the shedding cycle cutting through the “head” of the three-dimensional structure. Apart from this cut, we also get a cut between adjacent structures from the weak sweep events, with the condition u’<- urms. Using these conditions, on the phase-locked velocity fields, we effectively lock the structures in time, as well as in the spanwise direction. With this ,a clearer picture of the shedding process emerges. The flow is highly three-dimensional near reattachment and the shedding of the separation bubble is modulated in the spanwise direction owing to the three-dimensional hairpin like vortical structures in the flow. The separation bubble is seen bulged out and lifted high at locations where the head of the hairpin vortex passes, owing to the strong ejection of fluid caused by the vortical structure. On the other hand, outside the hairpin vortices, weak sweep events push the flow towards the wall and make it shallow and less prominent, with the shedding being very weak in this plane. From these observations, a three-dimensional picture of the flow is proposed.