@phdthesis{Puetz2023, author = {P{\"u}tz, Michele}, title = {Numerical investigation and extension of quadrature-based moment methods for population balances}, doi = {10.26127/BTUOpen-6575}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-65751}, school = {BTU Cottbus - Senftenberg}, year = {2023}, abstract = {Particulate systems can be described by a number density function (NDF) with respect to a vector of internal coordinates. The evolution of the NDF is governed by the typically high-dimensional population balance equation (PBE). A common approach to reduce the dimensionality of the problem is to solve only for a set of moments instead of the NDF. The derived system of moment equations, however, includes unclosed integral terms that still contain the unknown NDF. One way to close the system of moment equations is to approximate the unclosed integral terms using a Gaussian quadrature computed from the moments. The procedure of taking a set of moments to compute a Gaussian quadrature, which is, in turn, used to close the moment equations, is known as the quadrature method of moments (QMOM). It gave rise to an entire family of methods, the quadrature-based moment methods (QBMMs), which are the primary focus of this work. The presented research can be divided into three major parts. The first part involves the formulation of a common Lagrangian droplet breakup model for QBMMs and the numerical investigation with the QMOM as well as the more sophisticated extended QMOM (EQMOM). The results indicate that the approximations are reasonably accurate when at least six moment equations are solved, with the EQMOM providing no advantages for the investigated configurations. In the second part, a quadrature-based moment model for the effects of fluid turbulence on particle velocities is formulated. The resulting moment equations contain non-smooth integrands that are the source of large errors when using common QBMMs. As an alternative, the Gauss/anti-Gauss QMOM (GaG-QMOM) is proposed that uses the average of a Gaussian and an anti-Gaussian quadrature. Numerical studies show that the GaG-QMOM is able to significantly reduce the previously observed large errors. Another novelty proposed in this context is the modification of the second-order strong-stability preserving Runge-Kutta method to guarantee the preservation of moment realizability in the presence of phase-space diffusion. The third part is concerned with the numerical exploration of the core algorithm of most QBMMs in terms of performance and accuracy. The algorithm consists of, first, computing the recurrence coefficients of the orthogonal polynomials associated with a set of moments, second, solving a symmetric tridiagonal eigenvalue problem to obtain the quadrature nodes and weights, and third, evaluating the integral terms in the moment equations. The results indicate that the contribution of the first step to compute the recurrence coefficients from moments to the overall computational costs is negligible. Instead, the primary focus should be on the fast solution of the eigenvalue problem and, possibly, on the efficient implementation of the moment source term evaluation, which becomes important when second-order processes are considered.}, subject = {Numerical algorithms; Computational fluid mechanics; Orthogonal polynomials; Turbulence; Population balance equations; Numerische Algorithmen; Numerische Str{\"o}mungsmechanik; Orthogonale Polynome; Populationsbilanzgleichungen; Turbulenz; Numerische Str{\"o}mungssimulation; Str{\"o}mungsmechanik; Numerisches Verfahren; Orthogonale Polynome; Turbulente Str{\"o}mung}, language = {en} } @phdthesis{Hamede2023, author = {Hamede, Mohammed Hussein Haytham}, title = {The turbulent very wide-gap Taylor-Couette flow : experimental investigation}, doi = {10.26127/BTUOpen-6445}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-64456}, school = {BTU Cottbus - Senftenberg}, year = {2023}, abstract = {Die Taylor-Couette-Str{\"o}mung (TC), die Str{\"o}mung zwischen zwei konzentrischen, unabh{\"a}ngig voneinander rotierenden Zylindern, wird als perfektes Modell zur Untersuchung von Scherstr{\"o}mungen {\"u}ber konkaven Oberfl{\"a}chen verwendet und ist eines der paradigmatischen Systeme der Fluidphysik. In dieser Arbeit wird eine experimentelle Untersuchung der turbulenten TC-Str{\"o}mung in einer sehr breiten Spaltgeometrie mit einem Radiusverh{\"a}ltnis 𝜂 = 0,1 durchgef{\"u}hrt. Das physikalische und dynamische Verhalten der Str{\"o}mung wird in einer Geometrie untersucht, die vor der vorliegenden Studie kaum untersucht wurde, was diese Studie einzigartig macht. Ziel der Studie ist es, die Auswirkungen der Kr{\"u}mmung auf die TC-Str{\"o}mung zu verstehen, insbesondere in F{\"a}llen, in denen die Umfangsl{\"a}nge des inneren Zylinders kleiner ist als die Spaltbreite. Die Str{\"o}mung wird in den verschiedenen Rotationsregimen untersucht: gegenl{\"a}ufige, mitl{\"a}ufige und reine Innenzylinder-Rotationsregime bis zu Scher-Reynoldszahlen Re_s≤ 150000. Das Str{\"o}mungsfeld wurde mit Hilfe von Visualisierungstechniken qualitativ untersucht. Bei der Untersuchung der verschiedenen Str{\"o}mungsparameter zeigen sich bekannte koh{\"a}rente TC-Str{\"o}mungsmuster sowie neu beobachtete Muster, von denen wir annehmen, dass sie nur bei TC-Str{\"o}mungen mit sehr großem Spalt existieren. F{\"u}r eine detailliertere quantitative Untersuchung wurde eine zeitaufgel{\"o}ste Messung des Geschwindigkeitsfeldes mit der Hochgeschwindigkeits-Partikel-Image-Velocimetry-Technik durch die Endplatte des Systems durchgef{\"u}hrt. Die radialen und azimutalen Geschwindigkeitskomponenten in der horizontalen 2D-Ebene werden an verschiedenen axialen Positionen gemessen, um die axiale Varianz der Str{\"o}mung zu erfassen. Das aufgezeichnete Str{\"o}mungsfeld wird verwendet, um den Drehimpulstransport in Form der Quasi-Nusselt-Zahl (Nu_ω) zu berechnen. Die Ergebnisse zeigen ein Maximum der Nu_ω f{\"u}r niedrige gegenl{\"a}ufige Raten von -0,011 ≤ μ_max ≤ -0,0077, was mit großr{\"a}umigen Strukturen verbunden ist, die den gesamten Spalt {\"u}berspannen. Dar{\"u}ber hinaus nimmt Nu_ω f{\"u}r Gegenrotationsraten, die h{\"o}her als μ_max sind, ab, bis es einen Minimalwert erreicht, und steigt dann f{\"u}r h{\"o}here Gegenrotationsf{\"a}lle tendenziell wieder an. Das Raum-Zeit-Verhalten des turbulenten Str{\"o}mungsfeldes f{\"u}r die F{\"a}lle mit hoher Gegenrotation zeigt die Existenz neu beobachteter Muster neben der {\"a}ußeren Zylinderwand, die sich nach innen ausbreiten, den Drehimpulstransport verst{\"a}rken und zu einem zweiten Maximum im Transport f{\"u}r h{\"o}here Gegenrotationsraten f{\"u}hren. Das Raum-Zeit-Verhalten des turbulenten Str{\"o}mungsfeldes f{\"u}r die F{\"a}lle mit hoher Gegenrotation zeigt die Existenz von neu beobachteten Mustern neben der {\"a}ußeren Zylinderwand, die sich nach innen ausbreiten, den Drehimpulstransport verst{\"a}rken und zu einem zweiten Maximum des Transports f{\"u}r h{\"o}here Gegenrotationsraten f{\"u}hren. F{\"u}r den rein rotierenden inneren Zylinder skaliert der Impulstransport.}, subject = {Experimental fluid mechanics; Taylor-Couette flow; Rotating flow; Turbulence; Particle image velocimetry; Experimentelle Str{\"o}mungsmechanik; Taylor-Couette-Str{\"o}mung; Rotationsstr{\"o}mung; Turbulenz; Turbulente Str{\"o}mung; Str{\"o}mungsmechanik; Rotationsstr{\"o}mung; Taylor-Couette-Str{\"o}mung}, language = {en} } @phdthesis{Jozefik2016, author = {Jozefik, Zoltan}, title = {Application of ODT to turbulent combustion problems in incompressible and compressible regimes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-38653}, school = {BTU Cottbus - Senftenberg}, year = {2016}, abstract = {The one-dimensional turbulence (ODT) model is applied to a reactant - to - product counterflow configuration as well as to a shock tube configuration in non-reactive flow and in deflagration and detonation regimes. The model employed herein solves conservation equations for momentum, energy, and species on a one dimensional (1D) domain corresponding to the line spanning the domain between nozzle orifice centers in the counterflow configuration and corresponding to the tube length in the shock tube configuration. The effects of turbulent mixing are modeled via a stochastic process, while the Kolmogorov and reactive length and time scales are explicitly resolved. In the counterflow configuration, comparisons between model and DNS results for spatial mean and root-mean-square (RMS) velocity, temperature, and major and minor species profiles are shown. The ODT approach shows qualitatively and quantitatively reasonable agreement with the DNS data. Scatter plots and statistics conditioned on temperature are also compared for heat release rate and all species. ODT is able to capture the range of results depicted by DNS. However, conditional statistics show signs of underignition. To carry out the shock tube simulations, the ODT methodology is extended to include an efficient compressible implementation and a model for capturing shock-induced turbulence is presented. The necessary algorithmic changes to include compressibility effects are highlighted and the model for capturing shock-turbulence interaction is presented. To validate the compressible solver, results for Sod's shock tube problem are compared against a finite volume Riemann solver. To validate the model for shock-turbulence interaction, comparisons for a non-reactive and a reactive case are presented. First, results of a shock traveling from light (air) to heavy (SF6) with reshock have been simulated to match mixing width growth data of experiments and turbulent kinetic energy results from LES. Then, for one-step chemistry calibrated to represent an acetylene/air mixture, the interaction of a shock wave with an expanding flame front is simulated, and results with 2D simulation (2D-sim) data for flame brush formation and ensuing deflagration-to-detonation transitions (DDT) are compared. Results for the Sod shock tube comparison show that the shock speed and profile are captured accurately. Results for the nonreactive shock-reshock problem show that interface growth at all simulated Mach numbers is captured accurately and that the turbulent kinetic energy agrees in order of magnitude with LES data. The reactive shock tube results show that the flame brush thickness compares well to 2D-sim data and that the approximate location and timing of the DDT can be captured. The known sensitivity of DDT characteristics to details of individual Wow realizations, seen also in ODT, implies that model agreement can be quantified only by comparing Wow ensembles, which are presently unavailable other than in an ODT run-to-run sensitivity study that is reported herein.}, subject = {Turbulence; Combustion modeling; One dimensional turbulence (ODT); Counterflow; Shock tube; Turbulenz; Verbrennungsmodellierung; Gegenstrom; Stoßrohr; Turbulente Str{\"o}mung; Gegenstr{\"o}mung; Stoßwellenrohr; Simulation}, language = {en} } @phdthesis{Koenig2015, author = {K{\"o}nig, Franziska}, title = {Investigation of high Reynolds number pipe flow - CoLaPipe experiments}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-35392}, school = {BTU Cottbus - Senftenberg}, year = {2015}, abstract = {Investigations of high Reynolds number pipe flow is up to now a great challenge due to the complex mechanisms which appear in pipe flow turbulence. Hence, suitable experimental facilities are necessary to resolve turbulent dynamics and therewith to provide the knowledge for the understanding of such a simple shear flow. For this reason the recent thesis deals with conceptual design and setup of a new high Reynolds number pipe test facility further on named CoLaPipe - Cottbus Large Pipe. It also comprises first investigations on pipe flow obtained from the new CoLaPipe, which can be classified into 1.)calibration measurements to put the facility into service and 2.)continuative measurements to provide experimental results helping to understand pipe flow. The first results within the CoLaPipe show that this new experimental facility is suitable to investigate turbulence at high Reynolds numbers, where this conclusion can be drawn from intensive investigations on the development length of the flow either for natural and artificial transition. From further experiments on the evaluation of the wall friction velocity using different estimation methods great difficulties and variations in the calculated values are obtained. These deviations are directly related to the scaling behavior of the mean and fluctuating velocity, which is also shown within this thesis and intensively discussed. Among the discussion of the setup of the new CoLaPipe and the first experimental results this thesis contains a broad literature review with the focus on high and very high Reynolds numbers. Nevertheless, pipe flow at low and moderate Reynolds numbers is described as well.}, subject = {Turbulence; Pipe flow; High Reynolds number; Wind tunnel; Fluid dynamics; Turbulenz; Rohrstr{\"o}mung; Hohe Reynoldszahlen; Windkanal; Str{\"o}mungsmechanik; Windkanal; Rohrstr{\"o}mung; Turbulente Str{\"o}mung; Reynolds-Zahl}, language = {en} }