Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session PB: Turbulence Modelling IV |
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Chair: Oleg Vasilyev, University of Colorado Room: 101B |
Tuesday, November 24, 2009 11:40AM - 11:53AM |
PB.00001: Chasing eddies and their wall signature in turbulent boundary layers at Mach 3 through 14 I.B. Beekman, S. Priebe, M.P. Martin We use a direct numerical simulation database of turbulent boundary layers,\footnote{Martin, M.P., JFM, vol. 570, pp. 347-364, 2006}$^,$\footnote{Martin, M.P., AIAA Paper 2004-2337}$^,$\footnote{Beekman \& Martin, APS DFD08} statistical tools,\footnote{Brown \& Thomas, Phys. Fluids, vol. 20, pp 243-251, 1977} scientifically-rooted packet-pattern recognition,\footnote{Ringuette, Wu \& Martin, JFM, vol. 594, pp. 59-69, 2008} and validated visualization algorithms\footnote{O'Farrell, C. Senior Thesis, Princeton University 2008} to identify hairpin packets and their wall signature. We investigate the variation of time scales and length scales associated with coherent structures and the role of hairpin packets on the generation of skin friction, wall-pressure loading and heat transfer. [Preview Abstract] |
Tuesday, November 24, 2009 11:53AM - 12:06PM |
PB.00002: ABSTRACT WITHDRAWN |
Tuesday, November 24, 2009 12:06PM - 12:19PM |
PB.00003: A Correlation Matrix Approach to Esimtating Velocity Fields Using Sensor Measurements Dietmar Rempfer, Paritosh Mokhasi A new approach to estimating velocity fields from sensor measurements is proposed based on approximating the correlation of the unknown velocity fields with a sample ensemble of snapshots. Proper orthogonal decomposition (POD) is performed on the ensemble to extract the spatial eigenfunctions. If the POD coefficients are known at a certain instance in time, then the velocity field at that time can be estimated. The POD coefficients can be computed if the correlations between the ensemble and the velocity field are known. However, since the velocity field is not known, an extension of POD called ``episodic-POD'' is used to produce models that enable one to approximate the correlation between the unknown velocity fields at the ensemble based on sensor measurements taken from the domain. The episodic-POD analysis on the correlation matrix reveals that the underlying structure of the velocity correlation is low-dimensional even if the original flow is high-dimensional. Furthermore, the structures are seen to be similar for different problems indicating some form of universality. It is shown that the method is robust in the presence of noisy measurements and sparse temporal data. It is also proposed that this new approach suggests that solving a high-dimensional system could be replaced with solving a single low-dimensional system with multiple initial conditions. [Preview Abstract] |
Tuesday, November 24, 2009 12:19PM - 12:32PM |
PB.00004: Assessing Turbulent Convective Heat Transfer Effectiveness with POD-based low order models Markus Schwaenen, Andrew Duggleby The efficiency of convective turbulent heat transfer processes is significantly affected by turbulent flow structures. These either increase drag within the flow for the gain of higher heat transfer or need to be controlled in order to maintain a given surface temperature level for cooling applications. Proper Orthogonal Decomposition (POD) has proven to be a useful tool for the analysis of structures in turbulent flows. In the approach developed, we extend the use of POD by including the fluid temperature, thus making a quantitative assessment of the interaction between flow structures and surface heat transfer possible. Specifically, we use the low order flow description provided by POD to create a framework within one can identify the most important spatial or temporal flow structures that have undesired implications on the convective energy transport at hand. We achieve this by calculating enthalpy thicknesses based on fluctuating quantities from the most energetic mode pairs. The method has been applied to pin fin heat transfer which might exist, for example, in an internal gas turbine cooling passage. [Preview Abstract] |
Tuesday, November 24, 2009 12:32PM - 12:45PM |
PB.00005: Spatial Variable Thresholding for SCALES AliReza Nejadmalayeri, Oleg V. Vasilyev, Alexei Vezolainen, Giuliano De Stefano The Stochastic Coherent Adaptive Large Eddy Simulation (SCALES) is a novel wavelet-based approach that resolves energy containing turbulent motions using wavelet multiresolution decomposition and self-adaptivity. The extraction of the most energetic structures is achieved using wavelet thresholding filter with a priori prescribed threshold level. This strategy, although successful, has a major drawback: the thresholding criterion is global and does not fully utilize the spatial/temporal intermittency of the turbulent flow. In the current numerical effort, for the first time (to the best of our knowledge), the concept of physics-based spatially variable thresholding in the context of wavelet-based numerical techniques for solving PDEs is introduced. The procedure consists of tracking the wavelet thresholding-factor within a Lagrangian frame by exploiting a Lagrangian Path-Line Diffusive Averaging approach that uses linear averaging along characteristics. The results for incompressible flow around NACA 0015 airfoil show a very robust and fast methodology for adjusting the thresholding-factor based on dynamically important flow characteristics, for instance, the magnitude of vorticity or strain rate. [Preview Abstract] |
Tuesday, November 24, 2009 12:45PM - 12:58PM |
PB.00006: Coherent vortex simulation of 3D homogeneous isotropic turbulence Naoya Okamoto, Katsunori Yoshimatsu, Kai Schneider, Marie Farge, Yukio Kaneda Coherent vortex simulation based on the wavelet filtered Navier-Stokes equations are presented for three-dimensional decaying isotropic turbulence. The vorticity field is decomposed into coherent vortices and an incoherent background noise using an orthogonal wavelet representation. The time evolution of the coherent vortices is then integrated deterministically, while discarding the incoherent flow contributions at each time step is shown to be sufficient to model turbulent dissipation. The wavelet filter dynamically adapts to the flow evolution and thus changes with time. A safety zone is required to track the vortices and the small scales produced by their nonlinear interaction. Different strategies for choosing the safety zone are tested and their influence on the precision and efficiency is assessed. We show that an adequate choice allows to reduce the number of degrees of freedom by a factor 6 with respect to direct numerical simulation, while preserving the high order statistics of the flow. [Preview Abstract] |
Tuesday, November 24, 2009 12:58PM - 1:11PM |
PB.00007: Higher-order system analysis Woutijn Baars, Charles Tinney A higher-order system identification technique will be presented in the context of stochastic estimation, as it is quite useful in the field of (experimental) fluid dynamics. This higher-order spectral stochastic estimation technique was originally developed in the context of Systems Identification. It is shown how this technique defaults to spectral Linear Stochastic Estimation when only the linear kernels are computed. In case of higher-order computations, the system is constructed using a frequency-domain Volterra series and is expressed as a linear algebraic system of equations that are solved for the linear and higher-order transfer kernel coefficients. In the trade-off to seek for higher-order transfer kernels, the increased complexity restricts the analysis to single input/single output. POD based methods can be inserted to alleviate this void whereby time-varying POD coefficients of the output are estimated from POD coefficients of the input. Strengths and weaknesses of the current implementation of this technique will be discussed using simulated data and an application of this method to an axisymmetric jet flow to identify coherent turbulent structures. [Preview Abstract] |
Tuesday, November 24, 2009 1:11PM - 1:24PM |
PB.00008: Representing broad band effects by low order Galerkin models of fluid flows Gilead Tadmor, Bernd R. Noack, Michael Schlegel, Oliver Lehmann, Scott Kelley, Marek Marzynski We discuss a system reduction strategy for spectral and Galerkin models of incompressible fluid flows. This approach leads to dynamic models of lower order, based on a partition in slow, dominant and fast modes. In the reduced order models,slow dynamics are incorporated as nonlinear manifold consistent with mean-field theory. Fast dynamics are stochastically treated and can be lumped in eddy viscosity approaches. The employed interaction models between slow, dominant and fast dynamics respect momentum and energy balance equations in a mathematically rigorous manner - unlike unsteady Reynolds-averaged Navier-Stokes models or Smagorinsky-type reductions of the Navier-Stokes equation. The proposed system reduction strategy is employed to the cylinder wake benchmark. [Preview Abstract] |
Tuesday, November 24, 2009 1:24PM - 1:37PM |
PB.00009: Cycles and unstable manifolds in bursting Couette flow Lennaert van Veen, Genta Kawahara, Atsushi Matsumura Since the publication of a landmark paper by Kawahara and Kida on the relevance of unstable periodic solutions to shear flow in 2001, the scale of dynamical systems-type computations in turbulence research has increased spectacularly. Equilibrium and periodic solutions have been computed in great spatial detail for Couette flow, pipe flow and many other geometries. One of the main goals of these computations is to explain the process of turbulent bursting in shear flows. Often, this transition occurs in the presence of a asymptotically stable laminar flow, so ordinary bifurcation scenarios cannot explain them. Instead, the current focus is on so-called ``edge states,'' i.e. saddle-type equilibria or periodic solutions that appear to live on a boundary between turbulent and laminar behaviour in phase space. In principle, we should be able to clarify the bursting process if we know the geometry of the (un)stable manifolds of such states. However, the systematic computation of these manifolds is a hard task. We will present a recently developed algorithm for the computation of unstable manifolds and its adaption to shear flow, both in a toy model and in a full-scale simulation of turbulent Couette flow. [Preview Abstract] |
Tuesday, November 24, 2009 1:37PM - 1:50PM |
PB.00010: A-Posteriori Study of the Sensitivity Equation Method and Complex-Step Differentiation in Capturing Coherent Structures in the Sensitivity Field of a Planar Mixing Layer Mohsen Zayernouri, Meredith Metzger The performance of two techniques in computational sensitivity analysis, the sensitivity equation method (SEM) and complex-step differentiation (CSD), has been evaluated for the incompressible, two-dimensional, temporal mixing layer. This a-posteriori study aims to discover how well these two approaches capture the coherent structures in the sensitivity field, where the quantity of interest is the sensitivity of vorticity to changes in the Reynolds number, $Re_{\delta_0}$. In SEM, the governing equations are first differentiated with respect to the parameter of interest, in this case $Re_{\delta_0}$, then discretized and solved numerically to obtain the sensitivity coefficients. In CSD, the governing equations are treated as complex; and, the sensitivity coefficients are estimated by dividing the imaginary part of the velocity field by a small perturbation in the parameter of interest. In this manner, CSD avoids subtractive cancellation errors associated with finite difference approximations. Simulations were run at a baseline test case of $Re_{\delta_0}=200$ using an unsteady finite-volume-based fractional step algorithm. The results show that CSD has many advantages over SEM including ease of implementation, faster performance, and higher accuracy at a same resolution. [Preview Abstract] |
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