Generation of Nonhomogeneous Turbulent Velocity Fields by Modified Randomized Spectral Method
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GENERATION OF NONHOMOGENEOUS TURBULENT VELOCITY FIELDS BY MODIFIED RANDOMIZED SPECTRAL METHOD A. V. Aleksandrov,1 L. V. Dorodnitsyn,2 A. P. Duben’,3 and D. R. Kolyukhin4
UDC 519.245, 532.517.4
A new version of the synthetic turbulent velocity generator is proposed for simulation of turbulent flows. The method is fully stochastic and generates a statistically anisotropic and nonhomogeneous random field, which provides the initial and boundary conditions for the deterministic eddy-resolving model of turbulence. The simulation method has been tested on a three-dimensional problem of developed turbulent channel flow. Keywords: synthetic turbulence, anisotropic turbulence, stochastic simulation, Monte-Carlo method.
Introduction Reynolds-averaged Navier-Stokes (RANS) models are inadequate for present-day applications requiring simulation of turbulent gas and liquid flows. Eddy-resolving models – Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES) – are used with ever increasing frequency. At high Reynolds numbers, however, the use of DNS and LES is essentially restricted by their high computation costs. Simulation of the onset and development of turbulence remains a difficult task. The most promising approach at present relies on artificially generated (synthetic) turbulence with physical characteristics closely approximating real turbulence. This direction emerged in 1970 in the work of Kraichnan [1] and has been developing for several decades. Complex flows are currently calculated by combining the averaged model over the entire domain with a detailed LES description in a small flow subregion, where the eddy pattern has to be investigated [2–4]. This requires specification of turbulence fields as the LES inlet conditions, which is typically done with synthetic pulsation generators. Techniques for artificial turbulence generation include the spectral approach that constructs the field as the sum of Fourier harmonics; a digital “white noise” filter [5]; a synthetic eddy generator [6], and others. Starting with Kraichnan [1], the spectral methods have enjoyed the greatest popularity [7–10]. Most of the proposed methods generate an isotropic field of velocity pulsations. However, a nonhomogeneous and anisotropic field is required for the specification of interface conditions between the RANS and LES zones, where boundary layers and other flow nonhomogeneities essentially disrupt the isotropy of turbulence. The construction of a nonhomogeneous turbulence velocity field by the spectral approach typically starts with the generation of a homogeneous isotropic field. Then the field is scaled at each point of the physical space in accordance with a given field of the Reynolds stress tensor. 1
Keldysh Institute of Applied Mathematics, Moscow, Russia; e-mail: [email protected]. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia; e-mail: dorodn@ cs.msu.su. 3 Keldysh Institute of Applied Mathematics, Moscow, Russia; e-mail: [email protected]. 4 Trofim
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