Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session L27: Turbulence: RANS & Hybrid Modeling |
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Chair: Svetlana Poroseva, University of New Mexico Room: 2009 |
Monday, November 24, 2014 3:35PM - 3:48PM |
L27.00001: The determination of turbulence-model statistics from the velocity-acceleration correlation Stephen Pope In Reynolds-stress models, a primary unknown is the pressure--rate-of-strain; and, in velocity probability density function (PDF) models, a primary unknown is the conditional mean pressure gradient (conditional on velocity). Except from direct numerical simulations (DNS) of simple canonical flows, there is little information about these statistics. Currently, it is not possible to measure pressure with the necessary resolution, so there are no measurements of these important quantities. It is shown that essentially the same information can be obtained from the velocity-acceleration correlation and the Reynolds stresses. Since these correlations arise predominantly from the larger, energy-containing motions, they can be obtained experimentally (without Kolomorov-scale resolution), and from DNS, and from well-resolved large-eddy simulations (LES). In terms of the second moments of velocity and acceleration, expressions are given for the redistribution term in the Reynolds-stress equation, and for the drift term in the generalized Langevin model for the PDF. [Preview Abstract] |
Monday, November 24, 2014 3:48PM - 4:01PM |
L27.00002: New Models for Velocity/Pressure-Gradient Correlations in Turbulent Boundary Layers Svetlana Poroseva, Scott Murman To improve the performance of Reynolds-Averaged Navier-Stokes (RANS) turbulence models, one has to improve the accuracy of models for three physical processes: turbulent diffusion, interaction of turbulent pressure and velocity fluctuation fields, and dissipative processes. The accuracy of modeling the turbulent diffusion depends on the order of a statistical closure chosen as a basis for a RANS model. When the Gram-Charlier series expansions for the velocity correlations are used to close the set of RANS equations, no assumption on Gaussian turbulence is invoked and no unknown model coefficients are introduced into the modeled equations. In such a way, this closure procedure reduces the modeling uncertainty of fourth-order RANS (FORANS) closures. Experimental and direct numerical simulation data confirmed the validity of using the Gram-Charlier series expansions in various flows including boundary layers. We will address modeling the velocity/pressure-gradient correlations. New linear models will be introduced for the second- and higher-order correlations applicable to two-dimensional incompressible wall-bounded flows. Results of models' validation with DNS data in a channel flow and in a zero-pressure gradient boundary layer over a flat plate will be demonstrated. [Preview Abstract] |
Monday, November 24, 2014 4:01PM - 4:14PM |
L27.00003: Investigation of the pressure-strain-rate correlation using high-resolution LES of the atmospheric boundary layer Khuong Nguyen, Martin Otte, Edward Patton, Peter Sullivan, Chenning Tong We analyze the pressure-strain term in the Reynolds stress transport equation using large-eddy simulations of the atmospheric boundary layer (ABL). The simulations are implemented on computational meshes varying from $256^3$ to $1024^3$ grid points and employ several different SGS closures (Smagorinsky 1963; Sullivan et al. 1994; Kosovic 1997). The results highlight the influence of both shear and buoyancy on the pressure-strain-rate correlation. In the neutral (shear dominated) ABL, the behavior of the pressure-strain-rate correlation predicted by the Smagorinsky and Kosovic SGS models are consistent with the log-layer scaling and DNS results. In the strongly convective ABL, all three models predict behaviors for the pressure-strain-rate correlation that are consistent with the mixed- (outer-) layer scaling and field measurements. In cases where both shear and buoyancy are important, the highest-resolution runs are able to predict a combination of the log-layer scaling (near the wall) and the mixed-layer scaling (away from the wall), whereas the coarser-resolution runs are unable to capture this transition. The results are potentially useful for both Reynolds stress models and transport-equation-based SGS models for the convective atmospheric boundary layer. [Preview Abstract] |
Monday, November 24, 2014 4:14PM - 4:27PM |
L27.00004: Formulation and calibration of a stochastic model form error representation for RANS Todd Oliver, Bryan Reuter, Robert Moser It is well-known that RANS turbulence models fail to accurately represent the effects of turbulence on the mean flow for many important flows. We consider probabilistic representations of this model inadequacy for wall-bounded flows. The particular probabilistic representations considered here take the form of stochastic differential equations that are loosely based on the Reynolds stress transport equations, but include random forcing to represent uncertainty due to the closure problem. This model is disretized using finite elements and a priori uncertainty quantification studies are conducted using Monte Carlo sampling. The results demonstrate that the resulting uncertainties in the mean velocity scale as desired with Reynolds number. In addition to the random forcing, the model contains a number of uncertain parameters. We demonstrate that these can be calibrated using available DNS data. The model is further tested via comparison against additional DNS data outside of the orignal calibration set. [Preview Abstract] |
Monday, November 24, 2014 4:27PM - 4:40PM |
L27.00005: Low-Order Models For Assessing RANS Closures Daniel Israel Historically, most coefficients in RANS models have been calibrated to match the growth rates of certain canonical self-similar flows. However, for many of these flows, the growth rates observed in experiments and DNS vary widely. In fact, George (1986) argues that a universal self-similar solution does not exist. This would imply that RANS model calibration is specific to a particular experiment. Using classical integral methods to reduce RANS models to ODEs, it is possible to obtain a low-order dynamical system which can be used to study the approach to self-similarity for the model. Comparing the trajectory maps for such low-order models to data suggests that most, if not all, of the discrepancy between different experiments can be explained by transient deviations from self-similarity, and that there is indeed a universal self-similar behavior. Furthermore, such trajectory maps can be used to assess how well transient behavior due to the initial conditions in RANS calculations captures the experimentally observed flow physics. [Preview Abstract] |
Monday, November 24, 2014 4:40PM - 4:53PM |
L27.00006: An intermittency model for predicting roughness induced transition Xuan Ge, Paul Durbin An extended model for roughness-induced transition is proposed based on an intermittency transport equation for RANS modeling formulated in local variables. To predict roughness effects in the fully turbulent boundary layer, published boundary conditions for $k$ and $\omega$ are used, which depend on the equivalent sand grain roughness height, and account for the effective displacement of wall distance origin. Similarly in our approach, wall distance in the transition model for smooth surfaces is modified by an effective origin, which depends on roughness. Flat plate test cases are computed to show that the proposed model is able to predict the transition onset in agreement with a data correlation of transition location versus roughness height, Reynolds number, and inlet turbulence intensity. Experimental data for a turbine cascade are compared with the predicted results to validate the applicability of the proposed model. [Preview Abstract] |
Monday, November 24, 2014 4:53PM - 5:06PM |
L27.00007: Near Wall Treatment of the Variable Resolution Partially Averaged Navier-Stokes Model Pooyan Razi, Sharath Girimaji The objective of this work is to develop appropriate turbulence closures for bridging between different resolutions in the near-wall region. The development is made in the context of partially-averaged Navier-Stokes (PANS) method. Seamless transition from region of low-resolution near the wall to high-resolution away from the wall is controlled using the PANS filter parameter. The resolution variation introduces commutation effects which are modeled using additional terms in the turbulent kinetic energy equation. In addition, to conserve the total turbulent energy due to the interaction of unresolved and resolved flow fields, innovative strategies are evaluated for channel flow as well as flat plate boundary layer. This study identifies some important challenges regarding the numerical stability and appropriate implementation of the energy conservation principles. The preliminary results are shown to be encouraging. [Preview Abstract] |
Monday, November 24, 2014 5:06PM - 5:19PM |
L27.00008: Dynamic DDES On DES Type Grid Zifei Yin, Paul Durbin A dynamic procedure allows a DES formulation that we developed to adjust$\ C_{DES}$ for different flow configurations. Similarly to the dynamic Smagorinsky model, the grid is required to be fine enough to resolve a significant portion of the inertial range. In some cases, that requirement conflicts with the goal of DES to cut down computing cost. The current effort is therefore to determine a proper$\ C_{DES}$ value by approximately recovering some unresolved small scales from primary, filtered solution. Repeated test filtering is adopted here to compute the approximation of the unfiltered solution. The formulation is based on the dynamic$\ l^2w$ DDES model and different geometries with varies grid resolution are tested to determine the applicability of proposed formultion on DES type grids. [Preview Abstract] |
Monday, November 24, 2014 5:19PM - 5:32PM |
L27.00009: New hybrid turbulence modelling approach, with application to dynamic stall control Sigfried Haering, Robert Moser We present numerical studies of a stalled airfoil experiencing transitory flow control using a new hybrid RANS/LES modeling approach developed specifically for such challenging flow scenarios. Traditional hybrid approaches exhibit deficiencies when used for fluctuating smooth-wall separation and reattachment necessitating ad-hoc delaying functions and model tuning making them no longer useful as a predictive tool. Additionally, complex geometries and flows often require high cell aspect-ratios and large grid gradients as a compromise between resolution and cost. Such transitions and inconsistencies in resolution detrimentally effect the fidelity of the simulation. Our approach more naturally transitions between RANS to LES obviating the need for tuning and directly accounts for anisotropy and inhomogeneity in the flow and grid. The results of these simulations not only provide fundamental insight into experimentally observed stall control mechanisms but also display the versatility and accuracy of the new modeling method in simulating complex flow phenomena. [Preview Abstract] |
Monday, November 24, 2014 5:32PM - 5:45PM |
L27.00010: Scale dependence of Reynolds stress transport in wall-bounded turbulence at $Re_\tau= 5200$ Myoungkyu Lee, Robert D. Moser A direct numerical simulation (DNS) of turbulent channel flow has been performed to study high Reynolds number wall-bounded turbulence. In particular, in this talk we will focus on the characteristics of the terms in the Reynolds stress transport equations in two recent channel flow DNS at $Re_\tau=1000$ and $5200$. The $Re_\tau=5200$ case is at sufficiently high Reynolds number for there to be a significant scale separation between the near-wall and outer layer turbulence. A spectral analysis of the Reynolds stress transport terms shows how the inner- and outer-layer turbulence interact across scale. One striking result of this analysis is that over a broad range of $y$, the turbulent transport of turbulent kinetic energy occurs at scales that are proportional to $y$. There is also a weak direct interaction between the outer-layer and near-wall turbulence at large scales, presumably resulting in the large-scale modulation of near-wall turbulence. Further results from this spectral Reynolds stress transport analysis will be presented to explore the characteristics of turbulent, viscous and pressure effects. [Preview Abstract] |
Monday, November 24, 2014 5:45PM - 5:58PM |
L27.00011: A revisit of the equilibrium assumption for prediction of near-wall turbulence Farid Karimpour, Subhas Venayagamoorthy Assuming equilibrium between the rates of production ($P$) and dissipation ($\epsilon$) of the turbulent kinetic energy ($k$) is widely employed for prediction and modeling of turbulent flows. In this study, we revisit the consequence of using equilibrium assumption for prediction of near-wall turbulence. To this end, the relevant scales inherent in the turbulent viscosity ($\nu_t$) formulation of the standard $k$-$\epsilon$ model is derived. We show that such turbulent viscosity formulations are not suitable for modeling near-wall turbulence. Furthermore, by using the turbulent viscosity ($\nu_t$) formulation suggested by Durbin, we also show that the anisotropic Reynolds stress is correlated with the wall-normal, isotropic Reynolds stress. {\it `A priori'} tests are performed to assess the validity of the propositions using the direct numerical simulation (DNS) data of unstratified channel flow. The comparisons with the data are excellent and confirm our findings. [Preview Abstract] |
Monday, November 24, 2014 5:58PM - 6:11PM |
L27.00012: Evaluation of turbulence models for prediction of separated turbulent boundary layer under unsteady adverse pressure gradients Junshin Park, Donghyun You Predicitive capabilites of Reynolds-averaged Navier-Stokes (RANS) techniques for separated flow under unsteady adverse pressure gradients have been assessed using SST $k-\omega$ model and Spalart-Allmaras model by comparing their results with direct numerical simulation (DNS) results. Both DNS and RANS have been conducted with a zero pressure gradient, a steady adverse pressure gradient, and an unsteady adverse pressure gradient, respectively. Comparative studies show that both RANS models predict earlier separation and fuller velocity profiles at the reattachment zone than DNS in the unsteady case, while reasonable agreements with DNS are observed for steady counterparts. Causes for differences in the predictive capability of RANS for steady and unsteady cases, are explained by examining the Reynolds stress term and eddy viscosity term in detail. The Reynolds stress and eddy viscosity are under-predicted by both RANS models in the unsteady case. The origin of the under-prediction of the Reynolds stress with both RANS models is revealed by investigating Reynolds stress budget terms obtained from DNS. [Preview Abstract] |
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