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In this study, the performance of several RANS and hybrid LES/RANS turbulence models along with different CFD solvers (ANSYS Fluent, OpenFOAM and RapidCFD) is tested in terms of their ability to reproduce the flow downstream of a 90° pipe bend. The focus is on the temporal mean profiles downstream of the bend up to approximately 31 times the pipe's diameter D. The turbulence models' accuracy is evaluated by means of performance indicators and flow profiles in comparison to LDA measurements. The results demonstrate that the use of RANS models is suitable as long as the location of interest is in the vicinity of the bend up to approximately 10 D downstream of the bend. With increasing distance, the accuracy of the RANS models decreases, and the use of hybrid LES/RANS models is recommended.Three hybrid LES/RANS models are tested: the stress-blended eddy simulation (SBES) model as well as the Spalart-Allmaras-based and the k-omega SST-based improved delayed detached eddy simulation (IDDES) models. All three models show enhanced results for a distance to the bend >10 D. Additionally, it is found that in this geometry configuration, the IDDES models require a transient inlet. The flow separation due to the redirection inside the bend is too weak to generate turbulent fluctuations and a fast transition to full LES mode in the separation region. Due to the turbulent excitation at the inlet, the RANS region downstream of the bend is distinctly reduced, resulting in an enhanced performance of the hybrid IDDES models.

This work presents a robust method that minimises the impact of user-selected parameter on the identification of generic models to study the coherent dynamics in turbulent flows. The objective is to gain insight into the flow dynamics from a data-driven reduced order model (ROM) that is developed from measurement data of the respective flow. For an efficient separation of the coherent dynamics, spectral proper orthogonal decomposition (SPOD) is used, projecting the flow field onto a low-dimensional subspace, so that the dominating dynamics can be represented with a minimal number of modes. A function library is defined using polynomial combinations of the temporal modal coefficients to describe the flow dynamics with a system of nonlinear ordinary differential equations. The most important library functions are identified in a two-stage cross-validation procedure (conservative and restrictive sparsification) and combined in the final model. In the first stage, the process uses a simple approximation of the derivative to match the model with the data. This stage delivers a reduced set of possible library function candidates for the model. In the second, more complex stage, the model of the entire flow is integrated over a short time and compared with the progression of the measured data. This restrictive stage allows a robust identification of nonlinearities and modal interactions in the data and their representation in the model. The method is demonstrated using data from particle image velocimetry (PIV) measurements of a circular cylinder undergoing vortex-induced vibration (VIV) at $$\mathrm{Re}=4000$$ Re = 4000 . It delivers a reduced order model that reproduces the average dynamics of the flow and reveals the interaction of coexisting flow dynamics by the model structure.

Operation under stable conditions is an important prerequisite for gas turbine safety. While recent studies have focused primarily on acoustic design to avoid thermoacoustic instabilities, in the present study we shift the focus to improving stability margins by flame transfer function (FTF) modification. The flame transfer function of premixed flames is affected by various mechanisms such as variations in equivalence ratio, swirl fluctuations and shear layer instabilities. These mechanisms can be influenced by modifying parameters such as fuel distribution, injection location, swirl number or gas composition. Based on the Nyquist stability method we formulate criteria for how and at what frequencies the flame transfer function needs to be modified, in order to increase the stability margins of a thermoacoustic system. Gain and phase margin as well as the sensitivity function serve as measures of stability. The criteria are limited to single frequencies, which allows experimental FTF optimization with manageable effort. In the second part of this study it is shown that the Nyquist method can also be used as an efficient and compact way to determine whether the uncertainties of subsystems can affect the overall stability, without requiring eigenvalue calculations.

This study performs a linear analysis of a turbulent reacting methane-air jet flame, with the goal of predicting the response of the reacting flow to upstream acoustic actuation. Accounting for heat release fluctuations is a vital component when investigating thermoacoustic instabilities and flame noise in a linearized framework. Unlike previous studies this work develops and applies an active flame approach, meaning the heat release oscillations of the flame resulting from the acoustic fluctuations are taken into account. To yield an active flame approach in the linear framework, a combustion model needs to be linearized. It is demonstrated that linearizing Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) combustion models leads to closure problems, making their application in the linearized framework troublesome. Reynolds-averaged Navier Stokes (RANS) combustion models, however, prove to circumvent this problem, which makes them suitable candidates for this purpose. The RANS combustion models are linearized around the temporal mean flow of the turbulent jet flame, which is obtained by LES. An a priori analysis shows that a linearized RANS-Eddy Break Up (EBU) model is the best suited among all investigated combustion models for the investigated set-up and reproduces with high accuracy the fluctuations in reaction rate obtained in the LES. Furthermore, the linearized governing equations of the flow including the linearized EBU model for the reaction rate are solved for incoming acoustic perturbations. The response modes show that the reaction rate oscillations are caused by Kelvin-Helmholtz vortex rings, which perturb the jet flame. The results are in good agreement with the LES simulations in terms of the mode shapes of both reaction rate and velocity fluctuations.

The generation and turbulent transport of temporal equivalence ratio fluctuations in a swirl combustor are experimentally investigated and compared to a one-dimensional transport model. These fluctuations are generated by acoustic perturbations at the fuel injector and play a crucial role in the feedback loop leading to thermoacoustic instabilities. The focus of this investigation lies on the interplay between fuel fluctuations and coherent vortical structures that are both affected by the acoustic forcing. To this end, optical diagnostics are applied inside the mixing duct and in the combustion chamber, housing a turbulent swirl flame. The flame was acoustically perturbed to obtain phase-averaged spatially resolved flow and equivalence ratio fluctuations, which allow the determination of flux-based local and global mixing transfer functions. Measurements show that the mode-conversion model that predicts the generation of equivalence ratio fluctuations at the injector holds for linear acoustic forcing amplitudes, but it fails for non-linear amplitudes. The global (radially integrated) transport of fuel fluctuations from the injector to the flame is reasonably well approximated by a one-dimensional transport model with an effective diffusivity that accounts for turbulent diffusion and dispersion. This approach however, fails to recover critical details of the mixing transfer function, which is caused by non-local interaction of flow and fuel fluctuations. This effect becomes even more pronounced for non-linear forcing amplitudes where strong coherent fluctuations induce a non-trivial frequency dependence of the mixing process. The mechanisms resolved in this study suggest that non-local interference of fuel fluctuations and coherent flow fluctuations is significant for the transport of global equivalence ratio fluctuations at linear acoustic amplitudes and crucial for non-linear amplitudes. To improve future predictions and facilitate a satisfactory modelling, a non-local, two-dimensional approach is necessary.

The study investigates two effects, which can lead to a mitigation of entropy waves in a gas turbine combustor: Mean flow shear dispersion and turbulent mixing. Using a transport equation for coherent fluctuations of a passive scalar in combination with a k-ε turbulence model, the advection and turbulent diffusion of entropy waves is modeled. The method is applied to a flow in a duct of rectangular cross section, previously investigated with experimental and numerical means by Weilenmann et al. [1]. We analyze the impact of a steady jet in crossflow (JIC) in the rectangular duct on the mitigation of entropy waves by the mean flow shear dispersion mechanism. First, a comparison to Large Eddy Simulation (LES) results demonstrates the capability of the linearized approach to quantify the decay due to turbulent mixing and mean flow shear dispersion. The results further indicate that the inhomogeneous highly three dimensional flow profile and increased turbulence caused by the JIC significantly mitigates entropy waves due to the enhancement of the mean flow shear dispersion and turbulent mixing in comparison to a base line configuration without the JIC. Second, we investigate in a parameter study the effect of turbulent mixing on the mitigation of the entropy waves. It is shown that the results are highly case dependent. While in some situations an increase in turbulent mixing — as expected — leads to a mitigation of entropy waves, in other situations it may have the opposite effect. We demonstrate that this is the case if turbulent mixing annihilates entropy fluctuations selectively in those regions, which contribute significantly to mean flow shear dispersion.

The exhaust flow of a pulse detonation combustor (PDC) is investigated for different operating conditions. The PDC consists of two units: the deflagration to detonation transition section, and the ...

This study investigates the linear stability of a laminar premixed flame, anchored on a square cylinder and confined inside a channel. Many modern linear analysis concepts have been developed and validated around non-reacting bluff-body wake flows, and the objective of this paper is to explore whether those tools can be applied with the same success to the study of reacting flows in similar configurations. It is found that linear instability analysis of steady reacting flow states accurately predicts critical flow parameters for the onset of limit-cycle oscillations, when compared to direct numerical simulation performed with a simple one-step reaction scheme in the low Mach number limit. Furthermore, the linear analysis predicts a strong stabilising effect of flame ignition, consistent with documented experiments and numerical simulations. Instability in ignited wake flows is, however, found to set in at sufficiently high Reynolds number, and a linear wavemaker analysis characterises this instability as being driven by hydrodynamic mechanisms of a similar nature as in non-reacting wake flows. The frequency of nonlinear limit-cycle flame oscillations in this unstable regime is retrieved accurately by linear eigenmode analysis performed on the time-averaged mean flow, under the condition that the full set of the reacting flow equations is linearised. If, on the contrary, unsteadiness in the density and in the reaction rate are excluded from the linear model, then the congruence between linear and nonlinear dynamics is lost.

An investigation of shock diffraction through a non-quiescent background medium is presented using both experimental and numerical techniques. Unlike diffracting shocks in quiescent media, a spatial distortion of the shock front occurs, producing a region of constant shock angle. An example of this process arises in the exhaust from a pulse-detonation combustor. As the background velocity is increased, such as through the inclusion of a converging nozzle at the exhaust, the spatial distortion becomes more apparent. Numerical simulations using a compressible Euler solver demonstrate that the distortion is not due to the geometrical influence of the nozzle, but rather is a function of the magnitude of the background flow velocity. The distortion is studied using a modified geometrical shock dynamics formulation which includes the background flow and is validated against experiments. A simple model is presented to predict the shock distortion angle in the weak-shock limit. Finally, the axial decay behaviour of the shock is investigated and it is shown that the advection of the shock by the background flow delays the arrival of the head and tail of the expansion characteristic at the centreline. This leads to an increase in the rate of decay of the shock Mach number as the background flow velocity is increased.

Motivated by the recent success in finding coherent structures in turbulent flows and describing their noise emission using the Resolvent Analysis (RA), the method is applied to a turbulent jet flame at Re = 15 , 000 and a corresponding non-reacting flow to investigate their axisymmetric dynamics. The RA, which in this study assumes a passive flame and neglects compressibility effects, is based on the governing equations linearized around the temporal mean state. It is validated against Spectral Proper Orthogonal Decomposition (SPOD) obtained from time-resolved snapshots. Both the temporal mean state and the snapshots are obtained by Large Eddy Simulation (LES). The SPOD reveals that an axisymmetric, convective Kelvin–Helmholtz (KH) instability is the dominant hydrodynamic mechanism in the jet flame within a narrow frequency band and incorporates up to 40 % of the turbulent kinetic energy. Results show that the RA is capable of reproducing the mode shapes seen in the SPOD. The RA furthermore allows to address the origin of these hydrodynamic structures: While the corresponding KH mode in a non-reacting turbulent jet flow is most sensitive to perturbations in the nozzle boundary layer, the same dominant mode in the turbulent Bunsen flame is most receptive to perturbations in the region between the nozzle edge and the annular pilot burner. The results suggest that the strong density gradients in this region initiate perturbations in the baroclinic torque, which are feeding the KH mode. Finally, a linear stability analysis proves that the high sensitivity of the KH structure is due to resonance with stable linear eigenmodes, which explains its high energy content. By applying the RA to a turbulent reacting flow, this study opens up a new pathway in analyzing the role of hydrodynamic structures in reacting flows.

Physics-informed neural networks (PINNs) can be used to solve partial differential equations (PDEs) and identify hidden variables by incorporating the governing equations into neural network training. In this study, we apply PINNs to the assimilation of turbulent mean flow data and investigate the method's ability to identify inaccessible variables and closure terms from sparse data. Using high-fidelity large-eddy simulation data and particle image velocimetry measured mean fields, we show that PINNs are suitable for simultaneously identifying multiple missing quantities in turbulent flows and providing continuous and differentiable mean fields consistent with the provided PDEs. In this way, consistent and complete mean states can be provided, which are essential for linearized mean field methods. The presented method does not require a grid or discretization scheme, is easy to implement, and can be used for a wide range of applications, making it a very promising tool for mean field-based methods in fluid mechanics.

An efficient computational framework for the numerical simulation of multi-tube pressure-gain combustors for gas turbine applications is introduced. It is based on the open-source AMReX software platform (https://amrex-codes.github.io/amrex/), enhanced to allow for the flexible coupling of multiple computational domains with possibly different dimensionality. Here, six pulsed detonation tubes represented by an efficient one-dimensional model are coupled at their outlets to a threedimensional plenum reservoir. The plenum outlet can be partially blocked to simulate the flow resistance of the first stage of a turbine. This paper presents a validation of this computational setup against measurements obtained from a laboratory experiment with unblocked plenum, and a numerical simulation study of the flow generated by periodic sequential firing of the six detonation tubes into a plenum with a partially blocked exit cross section simulating the flow resistance of a turbine.

In order to determine the flame transfer function of a combustion system, different mechanisms have been identified that need to be modeled. This study focuses on the generation and propagation of one of these mechanisms, namely, the swirl fluctuations downstream of a radial swirl combustor under isothermal conditions. Swirl fluctuations are generated experimentally by imposing acoustic perturbations. Time-resolved longitudinal and crosswise particle image velocimetry (PIV) measurements are conducted inside the mixing tube and combustion chamber to quantify the evolution of the swirl fluctuations. The measured flow response is decomposed using spectral proper orthogonal decomposition to unravel the contributions of different dynamical modes. In addition a resolvent analysis is conducted based on the linearized Navier–Stokes equations to reveal the intrinsically most amplified flow structures. Both, the data-driven and analytic approach, show that inertial waves are indeed present in the flow response and an inherent flow instability downstream of the swirler, which confirms recent theoretical works on inertial waves. However, the contribution of the identified inertial waves to the total swirl fluctuations turns out to be very small. This is suggested to be due to the very structured forcing at the swirler and the additional amplification of shear-driven modes. Overall, this work confirms the presence of inertial waves in highly turbulent swirl combustors and evaluates its relevance for industry-related configurations. It further outlines a methodology to analyze and predict their characteristics based on mean fields only, which is applicable for complex geometries of industrial relevance.

In this paper, a new method is introduced to model the transport of entropy waves and equivalence ratio fluctuations in turbulent flows. The model is based on the Navier–Stokes equations and includes a transport equation for a passive scalar, which may stand for entropy or equivalence ratio fluctuations. The equations are linearized around the mean turbulent fields. These serve as the input to the model in addition to a turbulent eddy viscosity, which accounts for turbulent diffusion of the perturbations. Based on these inputs, the framework is able to predict the linear response of the flow velocity and passive scalar to harmonic perturbations that are imposed at the boundaries of the computational domain. These, in this study, are fluctuations in the passive scalar and/or velocities at the inlet of a channel flow. The code is first validated against analytic results, showing very good agreement. Then, the method is applied to predict the convection, mean flow dispersion, and turbulent mixing of passive scalar fluctuations in a turbulent channel flow, which has been studied in previous work with direct numerical simulations (DNS). Results show that our code reproduces the dynamics of coherent passive scalar transport in the DNS with very high accuracy and low numerical costs. Furthermore, we demonstrate that turbulent mixing has a significant effect on the transport of the passive scalar fluctuations. Finally, we apply the method to explain experimental observations of transport of equivalence ratio fluctuations in the mixing duct of a model burner.

The operation of a multitube pulse detonation combustor (PDC) evokes undesirable pressure fluctuations for a turbine downstream of the combustor. Pressure measurements in a downstream annular plenum reveal distinct pressure fluctuations. Although pressure peaks due to the shock waves emanating from the PDC tubes have been investigated in previous studies, pressure oscillations throughout the remaining cycle duration have received far less attention. Based on azimuthal and frequency mode decomposition of pressure signals at six circumferential positions, these oscillations are found to result from acoustic modes that are excited by PDC operation. This conclusion is verified by comparison with numerically calculated eigenmodes of the plenum. The impact of different operating parameters and the plenum outlet geometry on the acoustic oscillations are determined. The sequential firing of the PDC tubes at the lowest firing frequency in combination with a small blockage ratio was identified as the favorable configuration for the smallest acoustic fluctuations.

Varying the generator load of a hydro turbine results in short-term changes in the rotation frequency of the runner, leading inevitably to flow instability and strong flow swirling behind the turbine. This may lead to the formation of unsteady flow regimes featured by vortex instability of the swirling flow behind the runner, known as the precessing vortex core (PVC) Dorfler et al. (2012). This effect causes dangerous periodic pressure pulsations that propagate throughout the water column in the draft tube. The present study reports on stereo PIV measurements of the air flow field inside a transparent draft tube of a model hydro turbine for a wide range of operation conditions. The research is focused on the time-averaged flow properties (mean velocity field and the second-order moments of velocity fluctuations), pressure pulsations and coherent flow structures in the velocity field.

In the context of thermoacoustic instabilities, knowledge about the generation and transport of equivalence ratio fluctuations is highly important to correctly model their impact on the flame transfer function. In this work, spatially resolved equivalence ratio perturbations in the mixing section of an acoustically forced, partially premixed swirl burner typical of modern gas turbine combustors are investigated. Tunable diode laser absorption spectroscopy using a wavelength-modulation approach is applied to assess the spatially inhomogeneous equivalence ratio field in the radial direction. Particle image velocimetry is applied to measure the axial velocity field. Based on these results, a tomographic reconstruction is utilized to deduce the local fuel distribution at two axial locations. Integrated, global equivalence ratio fluctuations are calculated and compared to simple line-of-sight measurements. The influence of the forcing frequency and amplitude is investigated and good agreement was found between the different measurement approaches. Frequency dependent equivalence ratio perturbation generation mechanisms driven by air velocity fluctuations in the swirler, as well as pressure fluctuations at the fuel injector, are observed. Two different mixing transfer functions modeling diffusion and dispersion are compared to the results and reveal substantial differences, indicating a significant impact of coherent fluctuations of the transport velocity on the mixing that are not accounted for by either of the models.

A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics is separated into deterministic contributions representing the global mode and a stochastic contribution representing the intrinsic turbulent forcing. Stochastic models are developed that account for the interaction between the two and allow the determination of the dynamic properties of the flow from stationary data. The deterministic contributions are modelled by an amplitude equation, which describes the oscillatory dynamics of the instability, and in a second approach by a mean-field model, which additionally captures the interaction between the instability and the mean-flow corrections. The stochastic contributions are considered as coloured noise forcing, representing the spectral characteristics of the stochastic turbulent perturbations. The methodology is applied to a turbulent swirling jet with a dominant global mode. Particle image velocimetry measurements are conducted to ensure that the mode is the most dominant coherent structure, and further pressure measurements provide long time series for the model calibration. The supercritical Hopf bifurcation is identified from the linear growth rate of the global mode, and the excellent agreement between measured and estimated statistics suggest that the model captures the relevant dynamics. This work demonstrates that the sole observation of limit-cycle oscillations is not sufficient to determine the stability of turbulent flows, since the stochastic perturbations obscure the actual bifurcation point. However, the proposed separation of deterministic and stochastic contributions in the dynamical model allows the identification of the flow state from stationary measurements.

In gas turbine combustion systems, the reduction of emissions of harmful combustion by-products is a main development goal. This study provides a methodology to model NOX emissions effectively for varying levels of pilot fuel flows at different operational points. It combines one-dimensional flame simulations using detailed chemistry with a stochastic approach for equivalence ratio fluctuations to account for the effect of fuel-air unmixedness. This split allows for computationally fast variations of the gas inlet condition and the consideration of different shares of pilot gas. The generation of emissions is split into a share of prompt formation at the flame front and a slower formation mechanism, occurring within the combustion products in the post flame region. The influence of unmixedness of the fuel-air mixture on both effects is taken into consideration by means of probability density functions (PDFs) of the equivalence ratio. These are modeled on the basis of sampled values from Large Eddy Simulations at the flame front and adapted for different shares of pilot gas. It is shown that with a superposition of Gaussian PDFs the equivalence ratio distribution at the flame front resulting from the main gas supply and the pilot share can be well approximated. Measurement data from experiments in atmospheric conditions as well as emission measurements from high pressure tests are used to evaluate the model. Good agreement is found for atmospheric data, allowing for explanations on the effect of pilot fuel ratio on emissions. For elevated pressure, only qualitative trends could be reproduced. Hypotheses to explain this deviation are made that motivate further research.

Gas turbine combustors are commonly operated with lean premix flames, allowing for high efficiencies and low emissions. These operating conditions are susceptible to thermoacoustic pulsations, originating from acoustic-flame coupling. To reveal this coupling, experiments or simulations of acoustically forced combustion systems are necessary, which are very challenging for real-scale applications. In this work we investigate the possibility to determine the flame response to acoustic forcing from snapshots of the unforced flow. This approach is based on three central hypothesis: first, the flame response is driven by flow fluctuations, second, these flow fluctuations are dominated by coherent structures driven by hydrodynamic instabilities, and third, these instabilities are driven by stochastic forcing of the background turbulence. As a consequence the dynamics in the natural flow should be low-rank and very similar to those of the acoustically forced system. In this work, the methodology is applied to experimental data of an industry-scale swirl combustor. A resolvent analysis is conducted based on the linearized Navier-Stokes equations to assure analytically the low-rank behavior of the flow dynamics. Then, these dynamics are extracted from flow snapshots using spectral proper orthogonal decomposition (SPOD). The extended SPOD is applied to determine the heat release rate fluctuations that are correlated with the flow dynamics. The low-rank flow and flame dynamics determined from the analytic and data-driven approach are then compared to the flow response determined from a classic phase average of the acoustically forced flow, which allow the research hypothesis to be evaluated. It is concluded that for the present combustor, the flow and flame dynamics are low-rank for a wider frequency range and the response to harmonic forcing can be determined quite accurately from unforced snapshots. The methodology further allows to isolate the frequency range where the flame response is predominantly driven by hydrodynamic instabilites.

International audience; A framework for the computation of linear global modes, based on time stepping of a linearised Navier–Stokes solver with an Eulerian interface representation, is presented. The method is derived by linearising the nonlinear solver Basilisk, capable of computing immiscible two-phase flows, and offers several advantages over previous, matrix-based, multi-domain approaches to linear global stability analysis of interfacial flows. Using our linear solver, we revisit the study of Tammisola et al. (J. Fluid Mech., vol. 713, 2012, pp. 632–658), who found a counter-intuitive, destabilising effect of surface tension in planar wakes. Since their original study does not provide any validation, we further compute nonlinear results for the studied flows. We show that a surface-tension-induced destabilisation of plane wakes is observable which leads to periodic, quasiperiodic or chaotic oscillations depending on the Weber number of the flow. The predicted frequencies of the linear global modes, computed in the present study, are in good agreement with the nonlinear results, and the growth rates are comparable to the disturbance growth in the nonlinear flow before saturation. The bifurcation points of the nonlinear flow are captured accurately by the linear solver and the present results are as well in correspondence with the study of Tammisola et al. (J. Fluid Mech., vol. 713, 2012, pp. 632–658).

An annular plenum is integrated downstream of six pulse detonation combustors arranged in a canannular configuration. The primary purpose of the plenum is the mitigation of pressure and velocity fluctuations, which is crucial for operation with a downstream turbine. The flow inside the plenum is investigated by means of flush-mounted pressure transducers arranged in the axial and circumferential directions. The test rig is operated in different firing patterns at 16.7 Hz per tube. Two firing patterns are studied to characterize the shock dynamics inside the plenum. The obtained data allows for a better understanding of shock interaction and attenuation inside the plenum, as well as the quantification of pressure fluctuations at the plenum outlet. Furthermore, a comparison is made between piezoresistive and piezoelectric pressure transducers, showing the capability of piezoresistive transducers for dynamic pressure measurements. The performance of the piezoresistive transducers allows for time-resolved measurement of both static and total pressure at the exit of the plenum. Moreover, the plenum results in a significant attenuation of the leading shock wave while redistributing its energy both spatially and temporally.

In the field of gas-turbine engineering, entropy waves and fluctuations in fuel–air mixing are of significant importance. The impact of either mechanism on thermoacoustic stability of the engine and combustion noise considerably depends on how they are convected in the combustion chamber. In this work, a novel method is employed to analyse their convection. Both effects are modelled using a transport equation of a passive scalar linearized around the mean field. The linearized transport equation is discretized using finite elements. It is shown that turbulent passive scalar transport can be described by an eddy diffusivity in the linear framework. The method is furthermore validated against direct numerical simulation (DNS) of passive scalar transport in a turbulent channel flow. Taking the mean flow from the DNS as input, the method reproduces transport of periodic passive scalar fluctuations with high accuracy at negligible numerical expense. Previous studies investigated destructive interference of the passive scalar due to a non-uniform mean flow profile, a process termed mean flow shear dispersion. The method introduced in this study, however, allows us to additionally quantify the impact of molecular and turbulent diffusion. For the channel flow under investigation, mean flow shear dispersion is the dominant mechanism at low frequencies while, at higher frequencies, turbulent diffusion needs to be accounted for to reproduce the DNS results. Molecular diffusion, however, only has a minor effect on the overall convection in the turbulent channel flow.

The observation of a Hopf bifurcation in fluid dynamics is commonly associated with the occurrence of a global hydrodynamic instability. The increase of a control parameter above a critical value causes a change from a stable to an unstable flow condition. This behaviour is well understood for the occurrence of instabilities in laminar flows. In turbulent flows, however, the occurrence of hydrodynamic instabilities is similarly observed but less clear. The current work examines the use of stochastic models to describe the supercritical Hopf bifurcation of the global mode in a turbulent swirling jet. The consideration of the interaction between the global mode and the stochastic turbulent perturbations allows a consistent description of the experimental observations. This opens up extensive possibilities for describing and interpreting the occurrence of hydrodynamic instabilities in turbulent flows.

This work presents an automated process minimising input parameters for the study of turbulent flows. The goal is to gain insight into the flow dynamics by deriving a data-driven reduced-order model (ROM). Spectral proper orthogonal decomposition (SPOD) is used to efficiently separate the flow dynamics and project the flow field onto a low-dimensional subspace to represent the dominating dynamics with a reduced set of modes. A polynomial combinations of the temporal modal coefficients defines a function library to describe the dynamics by a linear system of ordinary differential equations. In a two-stages cross-validation procedure (conservative and restrictive sparsification), the most important functions are identified and combined in a final ROM. The process is demonstrated for PIV data of a circular cylinder undergoing vortex induced vibration (VIV) Re = 4000.

Shockless explosion combustion is a promising concept for implementing pressure gain combustion into a conventional gas turbine cycle. This concept aims for a quasi-homogeneous autoignition that induces a moderate rise in pressure. By this, considerable losses due to entropy generation by inherent shock waves of detonation-based concepts can be avoided. Since the ignition is not triggered by an external source but driven by chemical kinetics only, the homogeneity of the autoignition is very sensitive to local perturbations in equivalence ratio, temperature, and pressure that produce undesired local premature ignition. Therefore, the precise injection of a well-defined fuel profile into an convecting air flow is crucial to ensure a quasi-homogeneous ignition of the entire flammable mixture. The objective of this work is to demonstrate that the injected fuel profile is preserved throughout the entire measurement section. For this, two different control trajectories are investigated. Optical measurement techniques are used to illustrate the effect of turbulent transport and dispersion caused by boundary layer effects on the fuel concentration profile inside the combustor. Results from line-of-sight measurements by tunable diode laser absorption spectroscopy indicate that the transport of the fuel-air mixture is dominated by turbulent diffusion. However, comparisons to numerical calculations reveal the effect of dispersion towards the bounds of the fuel concentration profile. The spatially resolved distributions of the fuel concentration inside the combustor gained from acetone planar laser induced fluorescence replicates a typical velocity distribution of turbulent pipe flow in radial direction visualizing boundary layer effects. Comparing both methods provide deep insights into the transport processes that have an impact on the operation of the shockless explosion combustor.

The reduction of polluting NOx emission remains a driving factor in the design process of swirl-stabilized combustion systems, to meet strict legislative restrictions. In reacting swirl flows, hydrodynamic coherent structures, such as periodic large-scale vortices in the shear layer, induce zones with increased heat release rate fluctuations in connection with temperature peaks, which lead to an increase of NOx emissions. Such large-scale vortices can be induced by the helical coherent structure known as precessing vortex core (PVC), which influences the flow and flame dynamics of reacting swirl flows under certain operating conditions. We developed an active flow control system, which allows for a targeted actuation of the PVC, to investigate its impact on important combustion properties. In this study, the direct active flow control is used to actuate a PVC of arbitrary frequency and amplitude, which facilitates a systematic study of the impact of the PVC on NOx emissions. In the course of the present work, a perfectly premixed flame, which slightly damps the PVC, is studied in detail. Since the PVC is slightly damped, it can be precisely excited by means of open-loop flow control. In connection with time-resolved OH*-chemiluminescence and stereoscopic PIV measurements, the flame and flow response to PVC actuation as well as the impact of the actuated PVC on flow and flame dynamics are characterized. It turns out that the PVC rolls up the inner shear layer, which results in an interaction of PVC-induced vortices and flame. This interaction considerably influences the measured level of NOx emissions, which grow with increasing PVC amplitude in a perfectly premixed flame. Nearly the same increase is to be seen for a partially premixed flame. This in contrast to previous studies, where the PVC is assumed to reduce the NOx emissions due to vortex-enhanced mixing.