Propagation speed of inertial waves in cylindrical swirling flows

Thermo-acoustic combustion instabilities arise from feedback between flow perturbations and the unsteady heat release rate of a flame in a combustion chamber. In the case of a premixed, swirl stabilized flame, an unsteady heat release rate results from acoustic velocity perturbations at the burner inlet on the one hand, and from azimuthal velocity perturbations, which are generated by acoustic waves propagating across the swirler, on the other. The respective time lags associated with these flow–flame interaction mechanisms determine the overall flame response to acoustic perturbations and therefore thermo-acoustic stability. The propagation of azimuthal velocity perturbations in a cylindrical duct is commonly assumed to be convective, which implies that the corresponding time lag is governed by the speed of convection. We scrutinize this assumption in the framework of small perturbation analysis and modal decomposition of the Euler equations by considering an initial value problem. The analysis reveals that azimuthal velocity perturbations in swirling flows should be regarded as dispersive inertial waves. As a result of the restoring Coriolis force, wave propagation speeds lie above and below the mean flow bulk velocity. The differences between wave propagation speed and convection speed increase with increasing swirl. A linear, time invariant step response solution for the dynamics of inertial waves is developed, which can be approximated by a concise analytical expression. This study enhances the understanding of the flame dynamics of swirl burners in particular, and contributes physical insight into the inertial wave dynamics in general.</jats:p

Short- and long-term predictions of chaotic flows and extreme events: a physics-constrained reservoir computing approach.

We propose a physics-constrained machine learning method-based on reservoir computing-to time-accurately predict extreme events and long-term velocity statistics in a model of chaotic flow. The method leverages the strengths of two different approaches: empirical modelling based on reservoir computing, which learns the chaotic dynamics from data only, and physical modelling based on conservation laws. This enables the reservoir computing framework to output physical predictions when training data are unavailable. We show that the combination of the two approaches is able to accurately reproduce the velocity statistics, and to predict the occurrence and amplitude of extreme events in a model of self-sustaining process in turbulence. In this flow, the extreme events are abrupt transitions from turbulent to quasi-laminar states, which are deterministic phenomena that cannot be traditionally predicted because of chaos. Furthermore, the physics-constrained machine learning method is shown to be robust with respect to noise. This work opens up new possibilities for synergistically enhancing data-driven methods with physical knowledge for the time-accurate prediction of chaotic flows

Uncertainty quantification of growth rates of thermoacoustic instability by an adjoint Helmholtz solver

Thermoacoustic instabilities are often calculated with Helmholtz solvers combined with a low-order model for the flame dynamics. Typically, such a formulation leads to an eigenvalue problem in which the eigenvalue appears under nonlinear terms, such as exponentials related to the time delays that result from the flame model. The objective of the present paper is to quantify uncertainties in thermoacoustic stability analysis with a Helmholtz solver and its adjoint. This approach is applied to the model of a combustion test rig with a premixed swirl burner. The nonlinear eigenvalue problem and its adjoint are solved by an in-house adjoint Helmholtz solver, based on an axisymmetric finite-volume discretization. In addition to first-order correction terms of the adjoint formulation, as they are often used in the literature, second-order terms are also taken into account. It is found that one particular second-order term has significant impact on the accuracy of the predictions. Finally, the probability density function (PDF) of the growth rate in the presence of uncertainties in the input parameters is calculated with a Monte Carlo approach. The uncertainties considered concern the gain and phase of the flame response, the outlet acoustic reflection coefficient, and the plenum geometry. It is found that the second-order adjoint method gives quantitative agreement with results based on the full nonlinear eigenvalue problem, while requiring much fewer computations.Technological foundations for the design of thermally and mechanically highly loaded components of future space transportation systems (SFB TR40), Royal Academy of Engineering Research Fellowships Schem

Uncertainty quantification of growth rates of thermoacoustic instability by an adjoint Helmholtz solver

Thermoacoustic instabilities are often calculated with Helmholtz solvers combined with a low-order model for the flame dynamics. Typically, such a formulation leads to an eigenvalue problem in which the eigenvalue appears under nonlinear terms, such as exponentials related to the time delays that result from the flame model. The objective of the present paper is to quantify uncertainties in thermoacoustic stability analysis with a Helmholtz solver and its adjoint. This approach is applied to the model of a combustion test rig with a premixed swirl burner. The nonlinear eigenvalue problem and its adjoint are solved by an in-house adjoint Helmholtz solver, based on an axisymmetric finite-volume discretization. In addition to first-order correction terms of the adjoint formulation, as they are often used in the literature, second-order terms are also taken into account. It is found that one particular second-order term has significant impact on the accuracy of the predictions. Finally, the probability density function (PDF) of the growth rate in the presence of uncertainties in the input parameters is calculated with a Monte Carlo approach. The uncertainties considered concern the gain and phase of the flame response, the outlet acoustic reflection coefficient, and the plenum geometry. It is found that the second-order adjoint method gives quantitative agreement with results based on the full nonlinear eigenvalue problem, while requiring much fewer computations.Technological foundations for the design of thermally and mechanically highly loaded components of future space transportation systems (SFB TR40), Royal Academy of Engineering Research Fellowships Schem

Kinetic oxygen measurements by CVC96 in L-929 cell cultures

Generally animal and human cells use oxygen during their whole life. Consequently the oxygen use is a simple indicator to test the vitality of cells. When the vitality decreases by the delivery of toxic substances the decrease can be observed directly by the oxygen-use of the cells. To get fast information of the vitality of cells we have measured the O(2)-tension by testing a new model of a bioreactor, the Cell Vitality Checker 96 (CVC96), in practical application. With this CVC96, soon a simple test will exist for the measurement of the oxygen use. In this respect the question had to be answered whether the use in the laboratory is easy and whether oxygen as a parameter in the vitality test can also be applied in future for problems in the field of material testing

Transient vortex events in the initial value problem for turbulence

A vorticity surge event that could be a paradigm for a wide class of bursting events in turbulence is studied to examine how the energy cascade is established and how this event could serve as a new test of LES turbulence models. This vorticity surge event is tied to the formation of the energy cascade in a direct numerical simulation by the traditional signatures of a turbulent energy cascade such as spectra approaching -5/3 and strongly Beltramized vortex tubes. A coherent mechanism is suggested by the nearly simultaneous development of a maximum of the peak vorticity $\|\omega\|_\infty$, growth of the dissipation, the appearance of a helically aligned local vortex configuration and strong, transient oscillations in the helicity wavenumber spectrum. This coherence is also examined for two LES models, a traditional purely dissipative eddy viscosity model and a modern method (LANS$-\alpha$) that respects the nonlinear transport properties of fluids. Both LES models properly represent the spectral energy and energy dissipation associated with this vorticity surge event. However, only the model that preserves nonlinear fluid transport properties reproduces the helical properties, including Beltrami-like vortex tubes.Comment: 4 pages, 6 figure

Modeling heat transfer and skin friction frequency responses of a cylinder in cross-flow : a unifying perspective

The dynamic behavior of skin friction and heat release of a cylinder in pulsating cross-flow are investigated. Existing analytical solutions are presented as transfer functions versus frequency, known from control theory. Newly found expressions are given for Reynolds number ranges, where no appropriate model exist until now. These expressions are obtained by the combination of CFD simulation and system identification (CFD/SI). In the CFD/SI approach time series are generated by exciting inlet velocity fluctuations over a wide range of frequencies in one single CFD simulation. Time series are acquired for heat release, skin friction and velocity forcing, and then post-processed with system identification tools. Direct numerical simulations are conducted for mean flow Reynolds numbers between 0.1 and 40, solving the incompressible Navier-Stokes equations in a 2D domain using a finite volume approach. The system identification framework provides methods to identify a mathematical model for the response in heat release and skin friction to velocity fluctuations from data series. It can be confirmed that Bayly’s model for heat release fluctuations performs well at low Reynolds numbers. Lighthill’s model, often used in the assessment of Rijke tubes, is more accurate for high Reynolds numbers, but the time constant was underpredicted for Reynolds numbers of order 10. For the range above a Reynolds number of 0.4 a unifying model could be developed. This model especially excels at Reynolds numbers of order 10. Available models for skin friction usually match the simulated data up to a point, but do not give any dependence on Reynolds number which is corrected here. The expressions presented allow insight in the physics of the dynamic behavior of a cylinder in pulsating cross flow and also facilitate the use of these models in further investigations.Papers presented to the 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Costa de Sol, Spain on 11-13 July 2016