Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session NE: Turbulence: Modeling III |
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Chair: Gilead Tadmor, Northeastern University Room: Salt Palace Convention Center 151 D-F |
Tuesday, November 20, 2007 11:35AM - 11:48AM |
NE.00001: Using DNS Data to Validate the Steady-State 2D/3C Model of Turbulence in Plane Couette Flow Dennice Gayme, Beverley McKeon, Antonis Papachristodoulou, Bassam Bamieh, John C. Doyle Given the consensus that turbulent flow is characterized by coherent structures and observations of streamwise-elongated structures in numerical simulations and experiments (in the near wall region), we model the mean behavior of fully turbulent plane Couette flow using a streamwise constant projection of the Navier Stokes (NS) equations. This projection results in a two dimensional/three component ($2D/3C$) model comprised of two equations; one in terms of the spanwise/wall normal stream function $\psi(y,z,t)$ with noise forcing, and the other in terms of the stream-wise velocity, $u(y,z,t)$, and $\psi(y,z,t)$. This model is nonlinear but analytically more tractable than the full NS equations and was previously shown to have a single globally stable solution. In the present work we use the steady state $2D/3C$ model to explain features of the turbulent velocity field obtained from DNS data by Kawamura \textit{et al.} with $Re_w=3000$ ($Re_{\tau}=52$). [Preview Abstract] |
Tuesday, November 20, 2007 11:48AM - 12:01PM |
NE.00002: ABSTRACT WITHDRAWN |
Tuesday, November 20, 2007 12:01PM - 12:14PM |
NE.00003: Turbulence modeling based on a collisional Boltzmann equation Prakash Vedula, Rodney O. Fox Statistical descriptions of turbulent eddy motions by analogy with Boltzmann kinetic theory are well known in the literature, where relaxation models, such as the Bhatnagar-Gross-Krook (BGK) model, are used to account for the effects of eddy collisions. We propose to seek improvements to such approaches, through the use of a more detailed description of eddy collisions, via the Boltzmann collision operator, instead of currently used relaxation models. The resulting nonlinear, integro-differential, collisional Boltzmann equation for the evolution of the velocity distribution function is solved using a quadrature-based moment method, where the collision term can be analytically evaluated using multinomial expansions. This approach has the advantage of being able to describe distributions that are far from equilibrium, as it lacks a priori assumptions regarding equilibrium distributions. It can be also shown that the rate of dissipation of turbulent kinetic energy depends on an effective coefficient of restitution, which quantifies the degree of inelasticity of eddy collisions. Results based on return to isotropy of Reynolds stresses for homogeneous anisotropic turbulence, derived from the collisional Boltzmann equation, appear to be promising. [Preview Abstract] |
Tuesday, November 20, 2007 12:14PM - 12:27PM |
NE.00004: A model for the joint PDF for the scalar difference and the length scale in dissipation element analysis Lipo Wang, Norbert Peters Turbulent flow fields can be subdivided into dissipation elements, which are defined as the regions where trajectories share the same maximal and minimal points of a preset scalar. Among many parameters to describe the statistical properties of dissipation elements, two are of primary interest, namely the linear length, which is the straight line connecting the two extremal points and the scalar difference at the two points, respectively. The joint PDF of these two parameters allows to determine all conditional moments and thereby to provide the anomalous scaling exponents of higher structure functions. The model for the joint PDF is an extension of the model for the length scale distribution functions developed in Wang{\&}Peters, JFM 554, 457-475. The comparison of the results from the model with DNS data shows qualitatively a good agreement. [Preview Abstract] |
Tuesday, November 20, 2007 12:27PM - 12:40PM |
NE.00005: LES of Tilted Rayleigh-Taylor Using a Moment Closure Daniel Israel Traditional RANS closures solve directly for the mean statistics. For most canonical flows this reduces the problem to a set of 1-d steady, 1-d unsteady, or 2-d steady equations. All information about the unsteady turbulent structures is contained in a few (typically two) turbulent field variables. There are two situations that require switching to full 2- and 3-d time-dependent methods: first, a need to characterize details of the flow structures (perhaps due to complex initial or boundary conditions), and second, problems where the geometry itself is more complex. Conventional RANS has been found to sometimes produce unsteady structures for such flows, but if and when such structures appear does not seem to be linked to any physical process of the flow. A rational procedure for applying moment closure equations to such problems is under development and has been applied to the Rayleigh-Taylor unstable flow. In the current work the same method is applied to Rayleigh-Taylor in which the interface is tilted with respect to gravity. To simulate tilted Rayleigh-Taylor, the large scale overturning must be resolved in 2-d. The bubbles and spikes are likely to be amenable to a statistical treatment away from the wall, but may need to be explicitly resolved near the wall. The capabilities of the new closure are evaluated in the tilted Rayleigh-Taylor geometry, and compared to conventional RANS. [Preview Abstract] |
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