This thesis presents numerical investigations of two-dimensional single-phase turbulent jets and bubbly mixing layers using Reynolds-Averaged Navier-Stokes (RANS) equations. The behavior of a turbulent jet confined in a channel depends on the Reynolds number and geometry of the channel which is given by the expansion ratio (channel width to jet thickness) and offset ratio (eccentricity of the jet entrance). Steady solutions to the RANS equations for a two-dimensional turbulent jet injected in the middle of a channel have been obtained. When no entrainment from the channel base is allowed, the flow is asymmetric for a wide range of expansion ratio at high Reynolds number. The jet attaches to one of the channel side walls. The attachment length increases linearly with the channel width for fixed value of Reynolds number. The attachment length is also found to be independent of the (turbulent) jet Reynolds number for fixed expansion ratio. By simulating half of the channel and imposing symmetry, we can construct a steady symmetric solution to the RANS equations. This implies that there are possibly two solutions to the steady RANS equations, one is symmetric but unstable, and the other solution is asymmetric (the jet attaches to one of the side walls) but stable. A symmetric solution is also obtained if entrainment from jet exit plane is permitted. Fearn et al. (Journal of Fluid Mechanics, vol. 121, 1990) studied the laminar problem, and showed that the flow asymmetry of a symmetric expansion arises at a symmetry-breaking bifurcation as the jet Reynolds number is increased from zero. In the present study the Reynolds number is high and the jet is turbulent. Therefore, a symmetry-breaking bifurcation parameter might be the level of entrainment or expansion ratio. The two-dimensional turbulent bubbly mixing layer, which is a multiphase problem, is investigated using RANS based models. Available experimental data show that the spreading rate of turbulent bubbly mixing layers is greater than that of the corresponding single phase flow. The presence of bubbles also increases the turbulence level. The global structure of the flow proved to be sensitive to the void fraction. The present RANS simulations predict this behavior, but different turbulence models give different spreading rates. There is a significant difference in turbulence kinetic energy between numerical predictions and experimental data. The models tested include 𝘬—𝜖, shear-stress transport (SST), and Reynolds stress transport (SSG) models. All tested turbulence models under predict the spreading rate of the bubbly mixing layer, even though they accurately predict the spreading rate for single phase flow. The best predictions are obtained by using SST model. / Master of Science

<p>Turbulent mixing layers have been researched for many years. Currently, research is focused on studying compressible mixing layers because of their widespread applications in high-speed flight systems. While the effect of compressibility on the shear layer growth rate is well established, there is a lack of consensus over its effect on the turbulent stresses and hence warrants additional research in this area. Computational studies on compressible shear layers could provide a deep cognizance of the dynamics of fluid structures present in these flow fields which in turn would be viable for understanding the effects of compressibility on such flows. However, performing a Direct Numerical Simulation (DNS) of a highly compressible shear layer with experimental flow conditions is extremely expensive, especially when resolving the boundary layers that lead into the mixing section. The attractive alternative is to use Large Eddy Simulation (LES), as it possesses the potential to resolve the flow physics at a reasonable computational cost. Therefore the current work deals with developing a methodology to perform LES of a compressible mixing layer with experimental flow conditions, with resolving the boundary layers that lead into the mixing section through a wall model. The wall model approach, as opposed to a wall resolved simulation, greatly reduces the computational cost associated with the boundary layer regions, especially when using an explicit time-stepping scheme. An in house LES solver which has been used previously for performing simulations of jets, has been chosen for this purpose. The solver is first verified and validated for mixing layer flows by performing simulations of laminar and incompressible turbulent mixing layer flows and comparing the results with the literature. Following this, LES of a compressible mixing layer at a convective Mach number of 0.53 is performed. The inflow profiles for the LES are taken from a precursor RANS solution based on the k-ε and RSM turbulence models. The results of the LES present good agreement with the reference experiment for the upstream boundary layer properties, the mean velocity profile of the shear layer and the shear layer growth rate. The turbulent stresses, however, have been found to be underpredicted. The anisotropy of the normal Reynolds stresses have been found to be in good agreement with the literature. Based on the present results, suggestions for future work are also discussed.</p>

Wavlet analysis and its advantages in determining time-varying characteristics are discussed. The Morlet wavelet is defined and procedures for choosing its parameters are described. The recovery of modulation characteristics using the Morlet wavelet is demonstrated. Hydrodynamic linear stability is reviewed and its application to steady and unsteady mixing layers is discussed. Modulation effects are demonstrated by using the magnitude and phase of the wavelet coefficients. The time-varying characteristics of the most unstable modes are determined using the real part of the wavelet coefficients. It is found that mean flow unsteadiness increases the amplitude and phase modulation of the mixing layers. Synchronized variations of the two most unstable modes, the fundamental and the subharmonic, are also observed in the region of subharmonic growth. In a second application of wavelet analysis, the phase lag of the wavelet coefficients is used to determine the phase relation between the fundamental and the subharmonic in acoustically forced mixing layers. The results show that selective forcing affects the time-variations of the phase relation. In a third application, the magnitude and phase of the wavelet coefficients are used to decompose propagating waves measured at a single location. / Master of Science

We develop a physics-based reduced-order model of the aero-acoustic sound sources in reacting mixing layers as a method for fast and accurate predictions of the radiated sound. Instabilities in low-speed mixing layers are known to be dominated by the traditional Kelvin–Helmholtz (K–H)-type “central” mode, which is expected to be superseded by the “outer” modes as the chemical-reaction-based heat-release modifies the mean density, yielding new peaks in the density-weighted vorticity profiles. Although, these outer modes are known to be of lesser importance in the near-field mixing, how these radiate to the far-field is uncertain, on which we focus primarily, when the mixing layer is supersonic, but also report subsonic cases. On keeping the flow compressibility fixed, the outer modes are realized via biasing the respective mean density of the fast (oxidizer) or slow (fuel) side. In the linearized model that we use, the mean flow are laminar solutions of two-dimensional compressible boundary layers with an imposed composite turbulent spread rate, which we show to correctly predict the growth of instability waves by saturating them earlier, similar to in non-linear calculations, but obtained here via solving the linear parabolized stability equations (PSE). The chemical reaction is modeled via a single-step, single-product overall process which introduces a heat release term in the mean temperature equation. As the flow parameters are varied, modes that are unstable on the slow side are shown to be more sensitive to heat release, potentially exceeding equivalent central modes, as these modes yield relatively compact sound sources with lesser spreading of the mixing layer, when compared to the corresponding fast modes. In contrast, the radiated sound, obtained directly from the PSE solutions, seems to be relatively unaffected by a variation of mixture equivalence ratio, except for a lean mixture which is shown to yield a pronounced effect on the slow mode radiation by reducing its modal growth. For subsonic mixing layers, the sensitivity of central mode is explored, which in addition requires an acoustic analogy based method (e.g. the Lilley–Goldstein equations) to predict the sound from the linearized PSE sources, as used here, unlike in supersonic cases.

Στην παρούσα εργασία παρουσιάζονται πειραματικά αποτελέσματα των τρισδιάστατων διανυσμάτων των τυρβωδών πεδίων ταχύτητας και στροβιλότητας στην εγγύς περιοχή της τυρβώδους ορθογωνικής δέσμης με λόγο σύγκλισης 6. Οι τυρβώδεις ορθογωνικές ελεύθερες δέσμες έχουν πρακτικό ενδιαφέρον για την καύση, την πρόωση και τις περιβαλλοντικές ροές. Για την μέτρηση των μέσων και στατιστικών χαρακτηριστικών των συνιστωσών των δυο πεδίων σε διαφορετικές θέσεις στην εγγύς περιοχή της δέσμης χρησιμοποιήθηκε κεφαλή 12-αισθητήρων θερμού νήματος αποτελούμενη από τρεις κεφαλές 4 αισθητήρων. Η κεφαλή 12-αισθητήρων μετράει ταυτόχρονα τις τρεις συνιστώσες της ταχύτητας σε τρεις διαφορετικές θέσεις και επιτρέπει τον υπολογισμό των χωρικών παραγώγων του ανύσματος της ταχύτητας με την μέθοδο των πεπερασμένων διαφορών με ακρίβεια πρώτης τάξεως. Η κατασκευή της κεφαλής 12-αισθητήρων και η τεχνική μέτρηση βασίζεται στην εργασία των Lemonis & Drakos (1995) και Lemonis (1995) και έχει περαιτέρω βελτιωθεί στο Εργαστήριο Τεχνικής Θερμοδυναμικής του Πανεπιστημίου Πατρών. Οι μετρήσεις διεξήχθησαν σε αριθμό Reynolds, ReD = 21000 σε αποστάσεις κατά μήκος της ροής ίσες προς x/D =1, 3, 6 και 11, όπου D είναι το πλάτος του ακροφυσίου. Η αξιοπιστία της κεφαλής 12-αισθητήρων εκτιμήθηκε σε σύγκριση με τα αποτελέσματα της κεφαλής αισθητήρων X. Τα αποτελέσματα από τις μετρήσεις του πεδίου ταχύτητας και με τις δύο κεφαλές είναι σε καλή συμφωνία, εκτός από τις θέσεις όπου οι μεγάλες χωρικές κλίσεις της ταχύτητας και η τρισδιαστατότητα του πεδίου ταχύτητας υπονομεύουν τις μετρήσεις με την κεφαλή αισθητήρων Χ. Οι στατιστικές ιδιότητες των πεδίων της ταχύτητας και στροβιλότητας που υπολογίστηκαν από τις μετρήσεις με την κεφαλή 12-αισθητήρων εκτιμιούνται σε σύγκριση με πειραματικά και υπολογιστικά αποτελέσματα άλλων ερευνητών. Οι κατανομές των κυμαινόμενων πεδίων της ταχύτητας και στροβιλότητας δείχνουν ότι στην περιοχή του πυρήνα δυναμικού οι τιμές είναι αρκετά χαμηλές στον κεντρικό άξονα της δέσμης και αρκετά υψηλές στα διατμητικά στρώματα. Κατάντι της ροής οι διακυμάνσεις της ταχύτητας και στροβιλότητας μεταφέρονται από τα διατμητικά στρώματα προς το κέντρο και τις άκρες της δέσμης και οδηγούν στη συγχώνευση των διατμητικών στρωμάτων. Τα αποτελέσματα επιβεβαιώνουν επίσης τα υψηλά επίπεδα του ρυθμού εκφυλισμού (dissipation rate) στα διατμητικά στρώματα. Το ισοζύγιο της τυρβώδους ενέργειας παρουσιάζει σημαντικές διαφορές με το αντίστοιχο της επίπεδης δέσμης. Η σύγκριση των όρων της εξίσωσης της μέσης τετραγωνικής διακύμανσης της στροβιλότητας στη θέση x/D=11 δείχνει ότι η περιστροφή και η διάταση λόγω των διακυμάνσεων του ρυθμού παραμόρφωσης (strain rate) εξισορροπείται από τον ιξώδη εκφυλισμό της στροβιλότητας. Οι ανισοτροπίες στην εγγύς περιοχή της τυρβώδους ορθογωνικής δέσμης ερευνώνται και συζητούνται λεπτομερώς. Για την ερευνά της δομικής εξέλιξης της τυρβώδης ορθγωνικής δέσμης στην εγγύς περιοχή χρησιμοποιήθηκε επίσης και η μέθοδος PIV. Οι μετρήσεις με την μέθοδο PIV προσφέρουν το πλεονέκτημα της απεικόνισης της ροής μαζί με τη δυνατότητα καλύτερης κατανόησης των φαινόμενων της ροής, και ειδικότερα, πώς η δημιουργία, η αλληλεπίδραση και η συγχώνευση των στροβίλων συμβάλλουν στην ανάπτυξη της ορθογωνικής δέσμης. Τα αποτελέσματα των κατανομών φασμάτων ισχύος δείχνουν ότι μετά το τέλος του πυρήνα δυναμικού η ενισχυμένη συχνότητα αντιστοιχεί σε αριθμό Strouhal St=f•yc/U0≈0,11. Οι κατανομές της πυκνότητας ελικότητας στις περιοχές των διατμητικών στρωμάτων για x/D=3, 6, 11 δείχνουν μια τάση των ολικών διανυσμάτων της ταχύτητας και στροβιλότητας να ευθυγραμμιστούν. Από την άλλη, στις περιοχές των διατμητικών στρωμάτων για x/D=1 όπου το ολικό διάνυσμα της ταχύτητας είναι περίπου κάθετο προς την μέση ροή οι κατανομές παρουσιάζουν αντίθετη μορφή, όπως θα αναμενόταν. Η συλλογή πληροφοριών στην παρούσα έρευνα και η σύγκριση με τα ήδη υπάρχοντα στην βιβλιογραφία πειραματικά αποτελέσματα για τις τυρβώδες δέσμες αναμένεται να διευρύνουν περαιτέρω τη γνώση σχετικά με τη δομή των ελεύθερων διατμητικών ροών. / In the present work the three-dimensional velocity and vorticity vector fields in the near field of the rectangular turbulent jet with aspect ratio 6 have been experimentally investigated. Turbulent rectangular jets are prototypical free shear flows of practical interest in propulsion, combustion and environmental flows. The presented data, consisting of distributions of mean and statistical characteristics of the components of the two fields at several locations within the jet’s near field region, were obtained by using an in-house constructed 12-sensor hot wire probe consisting of three closely separated orthogonal 4-hot wire velocity arrays. The probe measures the three components of velocity simultaneously at three closely spaced locations. Spatial velocity derivatives are estimated using a forward difference scheme of first order accuracy. Streamwise velocity derivatives are estimated using Taylor’s frozen turbulence hypothesis. The 12-sensor construction and measurement technique relies upon previous work of Lemonis & Dracos (1995) and Lemonis (1995) and has been further improved and refined at the Laboratory of Applied Thermodynamics of the University of Patras. Measurements have been conducted in a jet with Reynolds number ReD = 21000 at nozzle distances, x/D =1, 3, 6 and 11, where D is the width of the nozzle. The performance of the 12-sensor probe is investigated in comparison with X-sensor probe measurements. Results referring to measurements of velocity with both sensors are in good agreement, except in locations where the steep velocity gradients and the three dimensionality of the velocity field undermine X-wire probe measurements. The statistical properties of the velocity-vorticity fields based on measurements with the 12-sensor probe are presented in comparison with several experimental and direct numerical simulation data of other researchers. Distributions of fluctuating velocity –vorticity fields show that in the potential core region the values are low on the centerline of the jet and quite high in the shear layers. Downstream the velocity-vorticity fluctuations spread from the shear layer towards the centre and the edge of the jet leading to merging of the two mixing layers. The results also confirm the high levels of dissipation rate in the shear layers. The turbulent energy balance shows important differences to that in plane jets. The budget of the transport equation for fluctuating enstrophy at x/D=11 indicates that the rotation and stretching by the fluctuating strain rate is balanced by the viscous dissipation of vorticity. The anisotropies in the near field of the turbulent rectangular jet are illustrated and discussed in detail. The structure development of a rectangular turbulent jet in the near field region has been also investigated experimentally using PIV. The results obtained with PIV measurements offer the advantages of flow visualization along with the possibility of better understanding the flow phenomena, in particular, how the formation, interaction and merging of vortices contribute to the development of the rectangular jet. The results of spectra distributions indicate that the most amplified frequency after the end of the potential core give rise to a Strouhal Number St=f•yc/U0≈0,11. In the regions of turbulent shear layers at x/D=3, 6, 11 the pdf’s of the relative helicity density h have shapes showing a preferred tendency for the total velocity and vorticity vectors to be aligned. On the other hand, in the regions of turbulent shear layers at x/D=1 where the total vorticity vector is more nearly orthogonal to the mean flow, the pdf’s show the opposite shape, as would be expected. Comparison and integration of the obtained information with the existing body of experimental evidence on turbulent rectangular jets is expected to enhance knowledge on the turbulence structure in free shear flows.

L’objectif de cette thèse est d’analyser le développement des instabilités secondaires bidimensionnelles et tridimensionnelles dans les couches de mélange à densité variable, incompressibles et à nombre de Froude infini. Dans ces conditions, la présence d’inhomogénéités de masse volumique modifie sensiblement la dynamique rotationnelle de l’écoulement et celle des instabilités secondaires sous l’action du couple barocline. Une analyse de stabilité linéaire non-modale est mise en oeuvre pour identifier les mécanismes physiques de croissance transitoire. Cette analyse permet également de prendre en compte le caractère instationnaire de la couche de mélange, absent dans l’analyse modale quasi-statique de Fontane (2005). Après établissement des équations de Navier–Stokes linéarisées directes et adjointes à densité variable, celles-ci sont utilisées dans une méthode d’optimisation itérative qui permet de déterminer les perturbations à croissance énergétique maximale. La première partie consiste en la description des perturbations optimales pour une couche de mélange homogène. Aux temps courts, lorsque la couche de mélange est quasi-parallèle, les perturbations optimales présentent de fortes amplifications transitoires, dont l’origine physique est due à la synergie des mécanismes classiques de Orr et de lift-up. Puis lorsque la couche s’enroule pour former un tourbillon de Kelvin–Helmholtz, les perturbations évoluent vers les instabilités tridimensionnelles elliptiques ou hyperboliques, selon le nombre d’onde latéral. Dans la deuxième partie, l’analyse est étendue aux couches de mélange à densité variable. Pendant la phase initiale de développement des perturbations optimales, les inhomogénéïtés de masse volumique ont une influence minime sur la croissance des perturbations. Ce n’est qu’une fois la couche de mélange enroulée que les effets de densité deviennent actifs, entraînant un supplément d’amplification significatif par rapport à la situation homogène. En particulier, le couple barocline favorise le développement des perturbations du côté du fluide léger du rouleau de Kelvin–Helmholtz. Enfin, lorsque le temps d’injection des perturbations est suffisamment retardé, la vorticité produite par le couple barocline favorise le développement d’une instabilité bidimensionnelle du type Kelvin-Helmholtz identifiée par Reinaud et al. (2000). / The purpose of this thesis is to analyse the development of two-dimensional and three-dimensional secondary instabilities in incompressible variable-density mixing layers, in the limit of infinite Froude number. Under these conditions, mass inhomogeneities alter significantly the rotational dynamics of the flow under the action of the baroclinic torque. A nonmodal stability analysis is implemented to identify the physical mechanisms of transient growth. This analysis allows to take into account the unsteady natureof the flow, which was absent in the quasi-static modal analysis (Fontane, 2005). After establishing of the direct and adjoint linearised Navier-Stokes equations for variable-density flows, they are used in an iterative optimization method to determine the perturbations that maximize their energy. The optimal perturbations are first obtained for a homogeneous time-evolving mixing layer. For times short enough, when the time-evolving mixing layer is almost parallel, optimal perturbations exhibit the largest transient growth. These amplifications arise from the synergy between the well-known Orr and liftup mechanisms. Once the mixing layer rolls up into a Kelvin–Helmholtz billow, the disturbances trigger the three-dimensional elliptical and hyperbolic instabilities. The analysis is then extended to variable-density mixing layers. During the initial development of optimal perturbations, mass inhomogeneities have no influence over the perturbations growth. Once the mixing layer has rolled up, the variable-density effects contribute significantly to the increase of the perturbation energy. In particular, the baroclinic torque enhances the development of perturbations in the light side of the Kelvin–Helmholtz billow. Finally, when the injection time of perturbations is delayed long enough, the baroclinic vorticity generation on the light side of the Kelvin–Helmholtz billow triggers a two-dimensional secondary Kelvin–Helmholtz instability, which has been identified by Reinaud et al. (2000).

This thesis is concerned with studies on spatially developing high speed mixing layers with twin objectives: (a) to provide enhanced and detailed understanding of spatial development of two-dimensional mixing layer emanating from splitter plate through large eddy simulation (LES, from now on) technique and (b) to evolve a consistent strategy for Unsteady Reynolds Averaged Navier-Stokes (URANS) approach to mixing layer calculations. The inspiration for this work arose out of the explanations that were being developed for the reduction in the mixing layer thickness with compressibility (measured by a parameter called convective Mach number, Mc). The reasons centered around increased stability, increase in compressible dissipation that was later discounted in favor of reduction in production and pressure-strain terms (with Mc, of course). These were obtained with direct numerical simulations (DNS) or LES techniques with homogeneous shear flow or temporal mixing layer. As apart, there was also a wide held view that using RANS (steady) techniques did not capture the compressibility effects when used in a way described above and so classical industrial codes for computing mixing- layer-embedded flows are unsuitable for such applications. Other important aspects that come out of the examination of literature are: the mixing layer growth is controlled in the initial stages by the double- boundary layer profile over the splitter plate and results in the mixing layer growth that is somewhat irregular due to doubling and merging of vertical structures. The view point of a smooth growth of the mixing layer is a theo- retical approximation arising out of the use of a smooth tan-hyperbolic profile that results at larger distances from the splitter plate. For all practical applications, it is inferred that the initial development is what is important because the processes of ignition and stable combustion occur close to the splitter plate. For these reasons, it was thought that understanding the development of the mixing layer is best dealt with using accurate spatial simulation with the appropriate initial profile. The LES technique used here is drawn from an OpenFOAM approach for dissimilar gases and uses one-equation Eddy Model for SGS stresses. The temporal discretization is second order accurate backward Euler and spatial discretization is fourth order least squares; the algorithm used for solving the equations is PISO and the parallelized code uses domain decomposition approach to cover large spatial domain. The calculations are performed with boundary layer profiles over the splitter plate and an initial velocity field with white noise-like fluctuations to simulate the turbulence as in the experiments. Grid independence studies are performed and several experimental cases are considered for comparison with measured data on the velocity and temperature fields as well as turbulent statistics. These comparisons are excellent for the mean field behavior and moderately acceptable for turbulent kinetic energy and shear stress. To further benefit from the LES approach, the details of the mixing layer are calculated as a function of four independent parameters on which the growth depends: convective Mach number (Mc = (U1 -U2)/ (a1 +a2)), stream speed ratio (r = U2=U1), stream density ratio (s = p2/p1) and the average velocity of the two streams ((U1+U2)=2) and examine the various terms in the equations to enable answering the questions discussed earlier. It is uncovered that r has significant influence on the attainment of self similarity (which also implies on the rate of removal of velocity defect in the double-boundary layer profile) and other parameters have a very weak influence. The minimum velocity variation with distance from the splitter plate has the 1/paxial distance behavior like in wakes; however, after a distance, departure to linear rise occurs and the distance it takes for this to appear is delayed with Mc. Other features such as the coherent structures, their merger or break up, the area of the structures, convective velocity information extraction from the coherent structures, the behavior of the pressure field in the mixing layer through the field are elucidated in detail; the behavior of the correlations between parameters (like pressure, velocity etc) at different points is used to elucidate the coherence of their fluctuating field. The effects of the parameters on the energy spectra have expected trends. An examination of the kinetic energy budget terms reveals that • the production term is the main source of the xx turbulence stress, whereas it is not significant in the yy component. • A substantial portion of this is carried by the pressure-velocity coupling from the xx direction to the yy direction, which becomes the main source term in the yy component. • Both, the production term as well as the pressure-velocity term show a clear decrease with increase in Mc. The high point of the thesis is related to using the understanding derived from an analysis of various source terms in the kinetic energy balance to evolve an unsteady Reynolds Averaged Navier Stokes (URANS) model for calculating high speed mixing layers, a subject that has eluded international research till now. It recognizes that the key feature affected by ompressibility is related to the anisotropy of the stress tensor. The relationship between stress component (_Txy) and the velocity gradient (Sxy) as obtained from LES is set out in the form of a simple relationship accounting for the effects of other parameters obtained earlier in this thesis. A minor influence due to _Tyy is extracted by describing its dependence on Sxy again as gleaned from LES studies. The needed variation of Prandtl and Schmidt numbers through the field is extracted. While the detailed variations can in fact be taken into account in URANS simulations, a simple assumption of these values being around 0.3 is chosen for the present simulations of URANS. Introduction of these features into the momentum equation gives the much expected variation of the reduction in the growth rate of the mixing layer with convective Mach number as in experiments. The relationships that can be used in high speed mixing layers are Introduction of these features into the momentum equation gives the much expected variation of the reduction in the growth rate of the mixing layer with convective Mach number as in experiments. This is then a suggested new approach to solve high speed mixing layers. While it can be thought that the principal contributions of the thesis are complete here, an additional segment is presented related to entropy view of the mixing layer. This study that considers the mixing layer with two different species expresses various terms involved in the entropy conservation equation and obtains the contribution of various terms on the entropy change for various Mc. It is first verified that the entropy derived from the conservation equation matches with those calculated from fluid properties, entropy being a state variable. It is shown that irreversible diffusion comes down the most with convective Mach number. Left: This image shows pictorially the flow of source of turbulent stress from the axial to the cross wise turbulent stress. Production (Σ) of turbulence happens mainly in the xx direction, a part of it is carried by the pressure-velocity correlation to the yy direction, which itself has a low production. With increasing Mc, both the production as well as the pressure-velocity correlation decrease. Right: This image shows the growth rate obtained from simulations scaled with the incompressible growth rate, of LES and RANS in the background of experiments (others). As is clear, the growth rate obtained is well within the band of experimental results.

Tato numerická studie je zaměřená na axisymetrickou pulzní trysku při zachování relativně nízkých Reynoldsových čísel a její fyzikální podstatu, která dosud nebyla zcela vysvětlena. Hlavním cílem práce bylo prozkoumat a zhodnotit vliv přidání periodického komponentu rychlosti ke stacionární složce rychlosti. Nejdříve byl řešen stacionární případ, poté byla do simulace přidána pulzace a byla vytvořena nestacionární simulace. Numerické řešení stacionárního případu bylo ověřeno pomocí asymptotického řešení, které předložil Hermann Schlichting [44]. Přesnost tohoto analytické řešení byla opravena na základě experimentálních poznatků Andradeho a Tsiena [1]. Pomocí této korekce je zmenšena oblast singularity řešení v blízkosti počátku proudění. Z matematického pohledu se v podstatě jedná korekcí prvního řádu, což bylo dokázáno Revueltou a spol [36]. Samotné analytické řešení bylo vytvořeno v MATLABu zatímco pro numerické řešení byl použit software Ansys Fluent. Při numerické simulaci byly Navier-Stokesovi rovnice integrovány ve své plné formě za pomoci algoritmu založeném na tzv. rovnici korekce tlaku. Pulzační tryska byla poté řešena pro různé parametry tak, aby bylo možné zhodnotit vliv jednotlivých parametrů na evoluci takto modulovaného proudu. Nakonec byla posouzena možná aplikace pulzních trysek v průmyslu s ohledem na možnost snížení emisí v průběhu spalovacího procesu.