Direct numerical simulation of pipe flow using a solenoidal spectral method

Tuğluk, Ozan
In this study, which is numerical in nature, direct numerical simulation (DNS) of the pipe ow is performed. For the DNS a solenoidal spectral method is employed, this involves the expansion of the velocity using divergence free functions which also satisfy the prescribed boundary conditions, and a subsequent projection of the N-S equations onto the corresponding dual space. The solenoidal functions are formulated in Legendre polynomial space, which results in more favorable forms for the inner product integrals arising from the Petrov-Galerkin scheme employed. The developed numerical scheme is also used to investigate the e ects of spanwise oscillations and phase randomization on turbulence statistics, and drag, in turbulent incompressible pipe ow for low to moderate Reynolds numbers (i.e. Re 5000) ).


Direct numerical simulation of pipe flow using a solenoidal spectral method
Tugluk, Ozan; Tarman, Işık Hakan (2012-05-01)
In this study, a numerical method based on solenoidal basis functions, for the simulation of incompressible flow through a circular-cylindrical pipe, is presented. The solenoidal bases utilized in the study are formulated using the Legendre polynomials. Legendre polynomials are favorable, both for the form of the basis functions and for the inner product integrals arising from the Galerkin-type projection used. The projection is performed onto the dual solenoidal bases, eliminating the pressure variable, si...
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In this thesis, a numerical code for calculating turbulent boundary layer parameters is developed. Two-dimensional turbulent flow over a rough flat plate with zero pressure gradient is numerically solved by using the integral method. Fluid mechanics formulations, such as momentum integral equation are coupled with the results of Nikuradse’s experiment. Throughout the calculation, turbulent boundary layer parameters, such as boundary layer thickness, displacement thickness, momentum thickness, local skin-fri...
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In this dissertation, efficient and reliable numerical algorithms for approximating solutions of multiphysics flow problems are investigated by using numerical methods. The interaction of multiple physical processes makes the systems complex, and two fundamental difficulties arise when attempting to obtain numerical solutions of these problems: the need for algorithms that reduce the problems into smaller pieces in a stable and accurate way and for large (sometimes intractable) amount of computational resou...
Analysis of Model Variance for Ensemble Based Turbulence Modeling
Jiang, Nan; Kaya Merdan, Songül; Layton, William (Walter de Gruyter GmbH, 2015-04-01)
This report develops an ensemble or statistical eddy viscosity model. The model is parameterized by an ensemble of solutions of an ensemble-Leray regularization. The combined approach of ensemble time stepping and ensemble eddy viscosity modeling allows direct parametrization of the turbulent viscosity co-efficient. We prove unconditional stability and that the model's solution approaches statistical equilibrium as t -> infinity; the model's variance converges to zero as t -> infinity. The ensemble method i...
Citation Formats
O. Tuğluk, “Direct numerical simulation of pipe flow using a solenoidal spectral method,” Ph.D. - Doctoral Program, Middle East Technical University, 2012.