Investigation of high-order, high-resolution methods for axisymmetric turbulent jet using ILEs

This Philosophiae Doctor thesis presents the motivation, objectives and reasoning behind the undertaken project. This research, study the capability of compressible Implicit Large Eddy Simulation (ILES) in predicting free shear layer flows, under different free stream regimes (Static and Co-flow jets). Unsteady flows or jet flows are non-uniform in structure, temperature, pressure and velocity. Turbulent mixing is of particular importance for the developing of this class of flows. As a shear layer is formed immediately downstream of the jet exhaust, an early linear instability involving exponential growth of small perturbations is introduced at the jet discharge. Beyond this development stage, in the non-linear Kelvin-Helmholtz instability region large scale vortex rings roll up, and their dynamics of formation and merging become the defining feature of the transitional shear flow into fully developed regime. This class of flows is particularly relevant to numerical predictions, as the extreme nature of the flow in question is considered as a benchmark; however, experimental data should be selected carefully as some results are controversial. To qualify the behaviour of unsteady flows, some important criteria have been selected for the analysis of the flow quantities at different regions of the flow field (average velocities, Reynolds stresses and dissipation rates). A good estimation of high-order statistics (Standard Deviation, Skewness and Kurtosis) correspond to mathematical steadiness and convergence of results. From the physical point of view, similarity analysis between jet’s wake sections reveals physical steadiness in results. Spectral analysis of the different regions of the flow field could be used as a sign that the energy cascade is correctly predicted or efficiently enough since this is where the smallest scales are usually present and which in effect require to be modelled by the different numerical schemes. The flow solver has been reviewed and improved. The former, a revised version of the reconstruction numerical schemes (WENO 5th and WENO 9th orders) has been performed and tested, the correspondent results have been compared against analytical data; the latter, correction of the method to compute the Jacobian of the transformation (singularity correction), by changing from the standard algebraic to geometric method, and augmented with transparent boundary condition, giving mathematical and physical meaning to the obtained results. The flow solver improvements and review have been verified and validated through simulations of a compressible Convergent-Divergent Nozzle (CDN), and the standard and a modified version of the Shock tube test cases, where the results are gained with minimal modelling effort. The study of numerical errors associated with the simulations of turbulent flows, for unsteady explicit time step predictions, have been performed and a new formula proposed. Ten different computational methods have been employed in the framework of ILES and computations have been performed for a jet flow configuration for which experimental data and DNS are available. It can be seen that a numerical error bar can be defined that takes into account the errors arising from the different numerical building blocks of the simulation method. The effects of different grids, Riemann solvers and numerical reconstruction schemes have been considered, however, the approach can be extended to take into account the effects of the initial and boundary conditions as well as subgrid scale modelling, if applicable. From the physical analysis several observations were established, revealing that differences in terms of jet’s core size are not an important parameter in terms of quantification and qualification of predictions, in other words, data should be reduced to the jet’s inertial reference system. Moreover, the comparative study has been performed to identify the differences between Riemann solvers (CBS and HLLC), Low Mach number Limiting/ Corrections (LMC), numerical reconstruction schemes (MUSCL and WENO) and spatial order of accuracy (2nd-order LMC, 5th-order LMC and 9th-order schemes) in combination with the most efficient cost/resolution discretization level (Medium mesh). The comparisons between results reveals for the Static and Co-Flow jets that the CBS MUSCL 5th-order LMC and the HLLC MUSCL 5th-order LMC as the most accurate schemes in predicting this class of flows, accordingly. Furthermore, the selected numerical methods show to be in accordance with the empirical (Static) and experimental (Co-flow) results in terms of resonance frequency and/or Strouhal number; also, the expected behaviour in terms of spectral energy decay rate throughout the jet’s central line is observed. To conclude the study of the Static jet case, a possible explanation for the jet’s buoyancy effect is presented.EThOS - Electronic Theses Online ServiceGBUnited Kingdo