The paper presents a novel view on the absolute instability phenomenon in heated variable density round jets. As known from literature the global instability mechanism in low density jets is released when the density ratio is lower than a certain critical value. The existence of the global modes was confirmed by an experimental evidence in both hot and air-helium jets. However, some differences in both globally unstable flows were observed concerning, among others, a level of the critical density ratio. The research is performed using the Large Eddy Simulation (LES) method with a high-order numerical code. An analysis of the LES results revealed that the inlet conditions for the velocity and density distributions at the nozzle exit influence significantly the critical density ratio and the global mode frequency. Two inlet velocity profiles were analyzed, i.e., the hyperbolic tangent and the Blasius profiles. It was shown that using the Blasius velocity profile and the uniform density distribution led to a significantly better agreement with the universal scaling law for global mode frequency.
The paper presents a new insight into understanding a mechanism to trigger the Crow and Champagne preferred mode. It is shown on the basis of numerical simulations that the preferred mode is established as a result of nonlinear interactions of primary structures generated by the Kelvin–Helmholtz instability. These interactions form larger coherent vortices characterized with frequency equal to half of the frequency of the primary perturbation. The paper shows that the shear-layer thickness at the nozzle exit constitutes a key parameter that influences significantly the jet response to an external forcing. The simulations were performed for jets with different shear-layer thicknesses. For the thicker shear layer the classical Kelvin–Helmholtz instability is observed. In this case the jet response to an external varicose forcing seems to be very similar to the experimental results of Crow and Champagne. The results presented shed new light on the preferred mode and the frequency selection mechanism confirming the suggestion of Crow and Champagne that nonlinearity is responsible for the preferred frequency. Significantly different results were obtained for a jet characterized by a thin shear layer. In this case the jet could be introduced into a self-sustained regime. External forcing with a frequency equal to the frequency of the natural self-sustained mode or with its subharmonic has practically no effect on the jet dynamics. The jet response to the forcing with frequencies different from the natural one depends on the forcing amplitude. A weak forcing disturbs the self-sustained mode leading to an interaction of two different modes that is observed in spectra with many frequencies related to both the self-sustained mode and the oscillations triggered by forcing. A stronger forcing suppresses the self-sustained mode and only the frequency components related to the stimulation are observed in the spectra. A mechanism responsible for the jet response to an external forcing under the self-sustained regime has not been extensively studied so far and a full understanding of these phenomena needs further studies and careful analysis.
The paper presents a detailed LES analysis of turbulent round jets dominated by the mechanism of Kelvin-Helmholtz (K-H) instability and the so-called self-sustained regime, which is characterised by large velocity fluctuations, reminiscent of the behaviour of excited jets. It is shown that the occurrence of this regime is largely conditioned by the type and parameters of the inlet jet velocity profile, i.e., the shear layer momentum thickness θ , turbulence intensity T i. A high order numerical code based on the combined pseudospectral / compact difference methods is used in the simulations. Analysis is performed for the Reynolds number Re = 1 × 10 4 with θ characterised by R/θ = 16, 20, 24, 28 and 32 (with R -jet radius) and for T i = 10 −2 , 10 −3 , 10 −4 . Two inlet velocity profiles are used in the simulations: hyperbolic tangent and Blasius. Comparisons focus on the axial velocity profiles and the spectra of the velocity signals. It is shown that in the self-sustained regime the results obtained with the Blasius profile are significantly closer to the experimental data. Sensitivity tests of the self-sustained regime on the sub-grid modelling are performed based on four well known models: classical and dynamic Smagorinsky, the filtered structure function model of Ducros et al. (JFM, 1996) and the relatively new model proposed by Vreman (PoF, 2004). It is shown that in the case of the classical Smagorinsky model an excess of sub-grid dissipation prevents the appearance of self-sustained velocity oscillations and in effect gives results significantly different from the remaining models. On the other hand, when the jets are dominated by K-H instability all the models lead to very similar solutions.
Purpose The purpose of the paper is to summarize recent achievements and suggest further research directions in numerical studies of round free jets with particular attention on the influence of the inlet parameters (mean velocity, turbulence intensity, length and time scales) on the jet dynamics. Design/methodology/approach The large eddy simulation (LES) and direct numerical simulation (DNS) are regarded as accurate tools which can support expensive and requiring sophisticated measurements techniques experimental studies. In the paper, the authors present challenges and recent findings related to the LES and DNS of jet type flows in isothermal, heated, excited and reactive conditions. Findings LES of the isothermal jet allowed to identify the new jet instability mechanism leading to the self-sustained oscillations and to determine conditions required to trigger this phenomenon. Numerical simulation on the low-density round jet captured the phenomenon of absolute instability with a very good agreement with the experimental findings. LES/DNS of excited jet exhibited bifurcating and blooming jet and showed that the jet can be directly controlled by excitation frequency what is crucial issue also for flame shape control. Originality/value The paper shows complexity of seemingly simple jet type flow and proves that despite a huge interest in these flows and relatively deep knowledge on the jet dynamics there are still some open issues requiring further studies.
The paper presents a new approximate deconvolution subgrid model for Large Eddy Simulation in which corrections to implicit filtering due to spatial discretization are integrated explicitly. The top-hat filter implied by second-order central finite differencing is a key example, which is discretised using the discrete Fourier transform involving all the mesh points in the computational domain. This discrete filter kernel is inverted by inverse Wiener filtering. The inverse filter obtained in this way is used to deconvolve the resolved scales of the implicitly filtered velocity field on the computational grid. Subgrid stresses are subsequently calculated directly from the deconvolved velocity field. The model was applied to study decaying two-dimensional turbulence. Results were compared with predictions based on the Smagorinsky model and the dynamic Germano model. A posteriori testing in which Large Eddy Simulation is compared with filtered Direct Numerical Simulation obtained with a Fourier spectral method is included. The new model presented strictly speaking applies to periodic problems. The idea of recovering a high-order inversion of the numerically induced filter kernel can be extended to more general non-periodic problems, also in three spatial dimensions.
The paper presents parametric studies of the first and second azimuthal absolute modes in annular non-swirling and swirling jets. The spatio-temporal linear stability analysis is applied to investigate an influence of governing parameters including axial velocity gradients in inner and outer shear layers, back-flow velocity, swirl number and shape of the azimuthal velocity. A new base flow is formulated allowing a flexible variation of the shape of axial and azimuthal velocity profiles. It is shown that the first helical absolute mode is governed mainly by the back-flow velocity and swirl intensity. A steepness of the inner shear layer can control the absolute mode frequency. The velocity gradient in the outer shear layer and the shape of the azimuthal velocity have rather limited impact on the absolute mode characteristics. Finally, it is shown that the second helical absolute mode can dominate the flow with a stronger swirl intensity.
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