Coherent structures in a swirl injector at Re  = 4800 by nonlinear simulations and linear global modes

Abstract

The large-scale coherent motions in a realistic swirl fuel injector geometry are analysed by direct numerical simulations (DNS), proper orthogonal decomposition (POD), and linear global modes. The aim is to identify the origin of instability in this turbulent flow in a complex internal geometry.The flow field in the nonlinear simulation is highly turbulent, but with a distinguishable coherent structure: the precessing vortex core (a spiraling mode).The most energetic POD mode pair is identified as the precessing vortex core. By analysing the FFT of the time coefficients of the POD modes, we conclude that the first four POD modes contain the coherent fluctuations. The remaining POD modes (incoherent fluctuations) are used to form a turbulent viscosity field, using the Newtonian eddy model.The turbulence sets in from convective shear layer instabilities even before the nonlinear flow reaches the other end of the domain, indicating that equilibrium solutions of the Navier-Stokes are never observed. Linear global modes are computed around the mean flow from DNS, applying the turbulent viscosity extracted from POD modes. A slightly stable discrete m = 1 eigenmode is found, well separated from the continuous spectrum, in very good agreement with the POD mode shape and frequency. The structural sensitivity of the precessing vortex core is located upstream of the central recirculation zone, identifying it as a spiral vortex breakdown instability in the nozzle. Furthermore, the structural sensitivity indicates that the dominant instability mechanism is the KelvinHelmholtz instability at the inflection point forming near vortex breakdown. Adjoint modes are strong in the shear layer along the whole extent of the nozzle, showing that the optimal initial condition for the global mode is localized in the shear layer.We analyse the qualitative influence of turbulent dissipation in the stability problem (eddy viscosity) on the eigenmodes by comparing them to eigenmodes computed without eddy viscosity. The results show that the eddy viscosity improves the complex frequency and shape of global modes around the fuel injector mean flow, while a qualitative wavemaker position can be obtained with or without turbulent dissipation, in agreement with previous studies.This study shows how sensitivity analysis can identify which parts of the flow in a complex geometry need to be altered in order to change its hydrodynamic stability characteristics.Key Words: † Email address for correspondence: outi-leena.tammisola@nottingham.ac.uk , and the exit velocity from the swirler (U E ). The coordinate system is also defined: the origin is at the centerline at the swirler exit location. The relative dimensions of the geometry are the same as in the numerical simulation, except that the numerical domain is longer in the downstream direction.

Adjoint Methods as Design Tools in Thermoacoustics

“…Importantly, they found that to improve the accuracy of stability calculations on mean flows the eddy viscosity should be extracted from the unsteady simulation. By extracting the eddy viscosity from direct numerical simulation (DNS), the sensitivity of the coherent structure oscillations to the shape of the injector in a helicopter engine combustion chamber (cold flow) was calculated in [116]. When the Reynolds number was based on the combined molecular and eddy viscosity, the prediction of the coherent structure frequency and shapes was markedly improved.…”

Onset of chaos in helical vortex breakdown at low Reynolds number

“…Such an analysis is found relevant to predict the frequency of limit cycle dynamics above the instability threshold in open flows presenting self-sustained oscillations. In contrast, global stability analysis around the base flow determines accurately the instability threshold but often fails to predict the correct frequencies (see, e.g., [32][33][34][35]).…”

Receptivity of the turbulent precessing vortex core: synchronization experiments and global adjoint linear stability analysis

“…The position roughly agrees with the determination of the wavemaker of similar swirling jet configurations from local LSA as well as global LSA. In Rukes et al (2016) and Tammisola & Juniper (2016), the wavemaker is located closely upstream of the stagnation point whereas in Kaiser et al (2018) the wavemaker region is approximately situated at the stagnation point itself.…”