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Attenuating and enhancing properties of the approximate deconvolution method based on higher - order explicit and compact filters

Caban L., Tyliszczak A.

Archives of Mechanics

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2023

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Vol. 75, nr 1-2

107--149

EN

We analyse the accuracy of a deconvolution (inverse filtering) method in 1D and 2D periodic domains. The deconvolution is performed by applying the iterative van Cittert method using explicit and compact filters of the 2nd to 8th order. We consider cases in which an approximate inverse filter G-1α formulated to deconvolve an original function from a filtered one (f = G⁎f) is constructed based on: (a) G the same as used to define f = G⁎f; (b) G different than the one used to define f = G⁎f. In case (a), the convergence rate of the deconvolution process is much better when compact filters are used. This is attributed to a flatter transfer function of this type of filter and thus a smaller deterioration of the input function f. Case (b) reflects a real situation in which the precise definition of a basic filter G used in f = G ⁎ f is unknown. We found that when G-1α is formulated based on G of a higher order than the one used to define f the reconstructed function f⁎ = G-1α⁎f is suppressed compared to the original function f. On the other hand, the deconvolution process performed with the use of G-1α defined based on G of a lower order than the order of the basic filter significantly amplifies the reconstructed function f⁎. As a result, the function f⁎ contains more energy than the function f, especially in the range of small and high-frequency scales. This effect is particularly strong when explicit filters of different orders are used. The impact of the filter type in the practical application of deconvolution is demonstrated based on large eddy simulations (LES) of a 2D decaying homogenous turbulent flow. LES combined with an approximate deconvolution method (ADM) for the computation of sub-filter terms shows better accuracy than in the case when these terms are modelled using the classical Smagorinsky model or when they are neglected (no-model approach). This analysis consists of comparisons of the evolution of total energy, energy spectra, and higher-order moments (variance, skewness, kurtosis) of the velocity components and vorticity. We found that more accurate results are obtained when the deconvolution is performed using the explicit filters even if the deconvolution process based on the compact filters was found to converge faster in 1D and 2D test cases. Most likely this is because in the performed LES the explicit filters correspond better to an unknown filter induced by discretisation.

2

Large Eddy Simulation of turbulent flowand heat transfer in a Kenics static mixer

Murasiewicz Halina, Zakrzewska Barbara

Chemical and Process Engineering

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2019

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Vol. 40, nr 1

87–-99

EN

CFD modelling of momentum and heat transfer using the Large Eddy Simulation (LES) approach hasbeen presented for a Kenics static mixer. The simulations were performed with the commercial codeANSYS Fluent 15 for turbulent flow of three values of Reynoldsnumber,Re=5 000, 10 000 and18 000. The numerical modelling began in the RANS model, where standardk−εturbulence modeland wall functions were used. Then the LES iterations started from the initial velocity and temperaturefields obtained in RANS. In LES, the Smagorinsky–Lilly modelwas used for the sub-grid scalefluctuations along with wall functions for prediction of flowand heat transfer in the near-wall region.The performed numerical study in a Kenics static mixer resulted in highly fluctuating fields of bothvelocity and temperature. Simulation results were presented and analysed in the form of velocity andtemperature contours. In addition, the surface-averaged heat transfer coefficient values for the wholeinsert length were computed and compared with the literature experimental data. Good compliance ofthe LES simulation results with the experimental correlation was obtained.

3

Application of the Lattice Boltzmann Method to the flow past a sphere

Kajzer A., Pozorski J.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

1091--1099

EN

The results of fully resolved simulations and large eddy simulations of bluff-body flows obtained by means of the Lattice Boltzmann Method (LBM) are reported. A selection of Reynolds numbers has been investigated in unsteady laminar and transient flow regimes. Computed drag coefficients of a cube have been compared with the available data for validation purposes. Then, a more detailed analysis of the flow past a sphere is presented, including also the determination of vortex shedding frequency and the resulting Strouhal numbers. Advantages and drawbacks of the chosen geometry implementation technique, so called “staircase geometry”, are discussed. For the quest of maximum computational effi- ciency, all simulations have been carried out with the use of in-house code executed on GPU.

4

LES numerical study on in–injector cavitating flow

Pyszczek R., Kapusta Ł. J., Teodorczyk A.

Journal of Power Technologies

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2017

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Vol. 97, nr 1

52--60

EN

In this paper a computational study on hexane flow in a fuel injector is presented. Large Eddy Simulation (LES) was used to capture the turbulent patterns present in the flow. The main aim was to investigate the cavitation phenomenon and its interaction with turbulence as well as the influence of injection pressure and backpressure on fuel mass flow and flow conditions. Analysis of the approach to define the outlet boundary conditions in terms of convergence time and fluid mass outflow oscillations formed a crucial part of the study. Numerical simulations were performed with AVL Fire CFD (Computational Fluid Dynamics) software. The Euler-Euler approach and multifluid model for multiphase flow modelling were applied. Injector needle movement was included in the simulation. Results show that the additional volumes attached to the nozzle outlets improved the convergence of the simulations and reduced mass outflow oscillations. Fuel mass flow at the outlets was dependent on inlet pressure, position of the needle and backpressure, while the influence of backpressure on fuel mass flow was negligible. The presence of the vapor phase at the exit of the nozzles did not affect average fuel mass flow. All the simulations showed interaction between the gaseous phase distribution and the turbulence of the flow.

5

Współczesne tendencje deterministycznego opisu turbulencji - metoda LES

Chmielniak T., Drobniak S.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2000

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z. 14

17-26

PL

W pracy przedstawiono współczesny stan badań w zakresie deterministycznego opisu turbulencji z zastosowaniem metody LES (arge Eddy Simulation). Omówiono ograniczenia tradycyjnego modelowania turbulencji opartego na ujęciu stochastycznym, które stały się powodem podjęcia prac zmierzających do rozwoju metod deterministycznego opisu turbulencji. Wykazano, że niedostateczne nadal możliwości obliczeniowe najszybszych nawet obecnie komputerów ograniczają możliwości uzyskania w pełni deterministycznych rozwiązań DNS (Direct Numerical Simulation) do zakresu niewielkich liczb Reynoldsa. Dlatego też w niniejszej pracy przedstawiono podstawy intensywnie obecnie rozwijanej techniki LES (Large Eddy Simulation), która wydaje się być rozsądnym kompromisem między dążeniem do uzyskania w pełni deterministycznych rozwiązań równania Naviera-Stokesa a możliwościami obliczeniowymi współrzędnych komputerów.

EN

The paper presents contemporary developments in the field of deterministic description of turbulence with special reference to Large Eddy Simulation (LES) methods. The limitations of conventional turbulence modelling based on stochastic methodology have been discussed and the reasons for development of deterministic approach were outlined. It has been shown that the computational power of the fastest available computers restrict the possible DNS (Direct Numerical Simulation) solutions to the range of small Reynolds numbers. Finally the basic assumptions have been formulated for the LES formalism, that seem to offer the reasonable compromise between the tendency towards the deterministic solution of Navier-Stokes equations and the existing computational resources