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Title: Synthetic turbulence based on the multi-scale turnover Lagrangian map
Author: Al-Bairmani, Sukaina
ISNI:       0000 0004 6497 4998
Awarding Body: University of Sheffield
Current Institution: University of Sheffield
Date of Award: 2017
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Synthetic turbulence refers to stochastic fields having characteristics of real hydro- dynamic turbulent flows, which has been useful in the modelling and simulation of turbulence, and for further understanding fundamental properties of turbulent motion. Synthetic turbulence aims to construct the field variables (such as velocity distributions) by simpler processes to reproduce characteristic features of turbulent fluctuations with a reduced computational cost in comparison with a formal numerical solution of the Navier-Stokes equations. A new approach of synthetic turbulence has been recently proposed, which showed that realistic synthetic isotropic turbulent fields could be generated using the Multi-scale turnover Lagrangian map (MTLM). The initial focus of this thesis is on studying the MTLM synthetic fields using the filtering approach. This approach, which has not been pursued so far, sheds new light on the potential applications of the synthetic fields in large eddy simulations and subgrid-scale (SGS) modelling. Our investigation includes SGS stresses, and SGS dissipations and related statistics, SGS scalar variance, and its relations with other quantities (such as the filtered molecular scalar dissipation). It is well-known that, even if a synthetic field had reproduced faithfully the multi-fractal statistics, it may not be able to produce the energy flux across the energy spectrum. Therefore, from the LES and/or SGS modelling perspective, many questions remain unclear, such as the PDF of the SGS dissipation, the amount of back-scattering, among others. They are addressed in this work. It demonstrates that using the MTLM is able to build a synthetic SGS model with a number of good features which many current SGS models (including those for the scalar flux) do not have. We also show that it has advantages in representing the filtered molecular scalar dissipation. In addition, we generalize the formulation of MTLM to include the effects of a mean scalar gradient on the scalar field. Our numerical tests provide the necessary proof that the effects of the mean gradient can be captured by MTLM. Furthermore, we investigate the effects of the input spectra on the statistics of the MTLM fields. We study the effects of the shape of the spectra by using truncated spectra and a model spectra (the Kovasznay spectra) as the input. The additional case, and the additional quantities we examine, have shedded light on how to apply the MTLM technique in simulations, as well as the robustness of the technique. The Constrained MTLM is a new technique generalizing the MTLM procedure to generate anisotropic synthetic turbulence in order to model inhomogeneous turbu- lence by using the adjoint formulation. Li and Rosales [107] derived the optimality system corresponding to the MTLM map and applied this method to synthesize two Kolmogorov flows. In this thesis, we derive a new optimality system to generate anisotropic synthetic turbulence according to the CMTLM approach in order to include the effects of solid wall boundaries, which were not taken into account in the last study. We consider the difference introduced by the solid wall, under the impermeable boundary conditions, where the normal components velocity field are zero, while the tangent components may be non-zero. To accomplish this task, we have modified the CMTLM procedure to generate a reflectionally symmetric synthetic field which serves as a model of the velocity field in a fully developed channel flow. That the MTLM procedure preserves the reflectional symmetries is proved, the adjoint optimality system with reflectional symmetry are derived. We aim to obtain accurate turbulent statistics, and compare our results with computed and experimental results. CMTLM procedure formulates MTLM procedure as an optimization problem with the initial Gaussian random field as the control and some known velocity field as the target. Thus, with the purpose to quantify the contributions of the adjoint operator in the modelling process, the effects of the control variable on the cost function gradient and the corresponding adjoint field is examined. Contours of the mean of the gradients of the cost functions and adjoint fields for three cases with data taken from synthetics CMTLM Kolmogorov flows and from CMTLM synthetics velocity field generated with DNS data as the target are computed. Finally, in order to define a new SGS model to simulate interactions between different length scales in turbulence, we will combine DNS data with Constrained MTLM method. Three data sets are truncated from DNS data with different degrees of resolution, filtered with the cutoff filter with large filter scale, which are then used as target fields to synthesize three CMTLM fields. The CMTLM fields are merged with these target fields. Data from the merged fields are used to predict the SGS quantities, and are compared with exact SGS quantities which have been computed from DNS field. In addition, the statistical geometry between the SGS and filtered quantities for real and predicted data are also investigated.
Supervisor: Li, Yi Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available