ETC2019 17th European Turbulence Conference Submission

14:00 Numerical Methods and Data Analysis 3

14:00 15 mins #257	Hybrid LES / RANS Paradigm for 3D Turbulent Mixing Filipe Pereira Soares, Fernando Grinstein, Dan Israel, Sharath Girimaji Abstract: The mixing of initially separate materials in a turbulent ﬂow by the small scales of turbulent motion is critical in many applications of interest to the DOE mission such as the implosion of an inertial confinement fusion (ICF) capsule. We are interested in detailed understanding of the consequences of material interpenetration, hydro-dynamical instabilities, and mixing arising from perturbations at accelerated material interfaces in turbulent flow applications exhibiting extreme geometrical complexity and broad range of length and time scales. In such applications, the practical simulation approach is large-eddy simulation (LES), where large energy containing structures are resolved, smaller structures are spatially filtered out, and effects of unresolved subgrid scales are modeled. On the engineering end of computation capabilities, unsteady Reynolds-Averaged Navier-Stokes (RANS) involving ensemble-averaged flow on coarser than LES grids are preferred for faster turnaround in full-scale configurations. Hybrid LES/RANS methodologies are the aerospace/automobile industrial standard for single-material wall-bounded flow applications [1]. Hybrid LES/RANS has not been explored for multi-material flow: we seek its extension to address variable-density compressible material-mixing issues. The present work aims to extend hybrid LES/RANS methodologies, originally proposed for affordable scale-resolving simulations (SRS) of wall-bounded turbulent flows, for their application to material-mixing problems. The Partially-Averaged Navier-Stokes (PANS) strategy is our particular present interest. The complete derivation of PANS equations is given in Germano [2], Girimaji [3], and Suman and Girimaji [4]. The PANS equations are based upon the scale-invariance property of the Navier-Stokes equations. This property has been first demonstrated by Germano [2] for incompressible flow, and later extended to compressible flow by Suman and Girimaji [4]. We build upon existing (non-hybrid and stand-alone) RANS and LES functionalities available in the LANL code xRAGE, a mature Eulerian flow solver for multi-material flows [5], with the ability to activate a variable-density RANS component based on the model by Besnard, Harlow, Rauenzahn, and Zemach (BHR) [6]. The BHR closures proposed by Stalsberg-Zarling and Gore [7] were selected to close the PANS governing equations. First, a robust and dynamical way of defining the RANS and LES region in the mixing flow is being developed. In existing hybrid LES/RANS methods, this model transition is based largely upon the wall distance that is no longer relevant in the mixing flow. PANS is one hybrid approach for mathematically defining a model that can locally adjust between LES and RANS. PANS versions exist for several RANS models for aerospace applications, but a variable-density / multi-material extension needs to be derived. Second, the behavior of the model through transition needs to be carefully examined in this context. One well known issue with hybrid models is that results can be very sensitive to how the energy exchange between modeled and resolved scales is handled in laminar-turbulent transition. We address modeling fundamental mixing dynamics, driven by: 1) forced and decaying isotropic turbulence, 2) non-equilibrium unsteady state-of-the-art shock-tube experiments. Relevant test cases [8] include the Taylor-Green vortex – prototyping transition and turbulence decay, and shock tube experiments – prototyping ICF shock-driven turbulent mixing mechanisms. Progress with ongoing developments – including a priori testing, will be reported. Los Alamos National Laboratory is operated by TRIAD LLC for US DOE NNSA. References 1. Frolich J & von Terzi, D.A., Hybrid LES/RANS methods for the simulation of turbulent Flows, Progress in Aerospace Sciences, 44, 349-77, 2008. 2. M. Germano, Journal of Fluid Mechanics 238, 325{336 (1992) 3. S. Girimaji, Journal of Applied Mechanics 73(3), 413{421 (2005) 4. S. Suman, S. Girimaji, Flow, Turbulence and Combustion 85(3-4), 383 (2010) 5. Gittings, M., Weaver, R., Clover, M., Betlach, T., Byrne, N., Coker, R., Dendy, E., Hueckstaedt, R., New, K., Oakes, W.R., Ranta, D., Stefan, R. 2008, The RAGE Radiation-Hydrodynamic Code, Comput. Science & Discovery 1, 015005. 6. D. Besnard, F. Harlow, R. Rauenzahn, C. Zemach, Turbulence Transport Equations for Variable-Density Turbulence and Their Relationship to Two-Field Models. LANL Tech. Rep. LA-12303-MS, DE92 017292 (1992) 7. K. Stalsberg-Zarling, R. Gore, The BHR2 Turbulence Model: Incompressible Isotropic Decay, Rayleigh-Taylor, Kelvin- Helmholtyz and Homogenous Variable Density Turbulence. LANL Tech. Rep. LA-UR-11-04773 (2011). 8. Grinstein, F.F., Saenz, J.A., Dolence, J.C., Masser, T.O., Rauenzahn, R.M., Francois, M.M., https://doi.org/10.1016/j.camwa.2018.05.008.
14:15 15 mins #326	Spatial Hierarchy Detection in Large Scale Coherent Structures Ido Ruhman, Ian Jacobi Abstract: The coherent structures of wall-bounded flows are inherently hierarchical, an observation made famous in Townsend's attached eddy framework and verified through subsequent studies of self-similar organization. Within the hierarchy of coherent structures, those with length scales, lambda, on the order of the boundary layer thickness, delta, have been shown to contribute strongly towards kinetic energy and Reynolds stresses. And within these large-scale motions, long meandering `super-structures' have been been shown to exert a significant modulating influence on smaller-scale, near-wall structures. The origins of these super-structures remain somewhat elusive, whether they result from the `bottom up' organization of small scale structures, like hairpins, into packets, or from the `top-down' influence of the outer flow. The inter-relationship between different scale motions in turbulence has thus received significant attention, largely via temporal filtering of single-point measurements. In the present research, we exploit spatial, wavelet-based, cluster-detection techniques from the world of astrophysics and network theory in order to define hierarchies of coherent structures within large-scale superstructures and measure their dynamics. Spatially resolved DNS measurements of a turbulent channel flow are analyzed via a continuous wavelet transform in order to establish a set of localized coherent motions of different scales, which are then classified into hierarchies by cluster thresholding techniques. The dynamic properties of different scales within each hierarchy are then explored in the context of spatial modulation relationships between large- and small-scale motions. The novel use of spatial wavelets and cluster-detection algorithms provides a new tool for the study of scale interactions in turbulence.
14:30 15 mins #502	Characterization of a hydrodynamic instability from experimental data using stochastic reduced order modeling Moritz Sieber, C. Oliver Paschereit, Kilian Oberleithner Abstract: The work presented here originates from the experimental observation of hydrodynamic instabilities in turbulent flows. The scope is the identification of the transition from a stable to an unstable state of a flow due to the change of a control parameter. This bifurcation will be characterized from experimental observations of the stationary flow at different operation conditions. The challenge for this approach is the separation of the deterministic contributions originating from the hydrodynamic instability and the stochastic perturbations introduced by the background turbulence. The principal approach is based on the method by Friedrich et al. [1] to identify model equations from experimental data. However, the successful application and extension of this method by Noiray and Schuermans [2] for thermo-acoustic instabilities in gas turbine combustors inspired us to use the approach for hydrodynamic instabilities. In the present application, the dynamics of the flow in the vicinity of the bifurcation point are modelled by the Stuart-Landau equation with an additional random forcing that accounts for the turbulent perturbations. The resulting stochastic differential equation is transformed to obtain an analytical expression for the probability density function of basic flow variables. The comparison of this analytical solution against experimental probability density functions allows the determination of the flow states from measurement data. The approach is exemplified from generic data to identify the limits of applicability with respect to the noise intensity and noise time scale. The later property describes the deviation from pure white noise forcing towards a noise with attenuation at high frequencies that is more consistent with turbulent forcing. The analysis indicates that the noise intensity might be relatively large but that the time scales of the hydrodynamic instability and the noise forcing must be well separated. The approach is also demonstrated for high-speed PIV and pressure measurements of the helical instability found in the swirling jet undergoing vortex breakdown [3]. The use of the stochastic reduced order modeling allows to clearly identify the transition of the flow. Furthermore, there are several experimental observations that are misleading when considered as classical bifurcation scenario. However, the assessment as a noise driven bifurcation explains these deviations and is much better in line with the experimental observation. The presented work might therefore inspire other researchers to interpret their results in light of mixed deterministic stochastic dynamics in order to explain odd experimental observations.
14:45 15 mins #14	Statistical properties of the filtered turbulence Markus Klein, Christian Kasten, Massimo Germano Abstract: The filtering approach is a simple data analysis technique based on the separation of scales produced by a filter F. Its main field of application is the interpretation of underesolved databases produced by numerical codes. A simple assumption usually adopted to extract the statistics from the filtered data is that F preserves the statistical averages, EF = E, where E is the ensemble mean operator. In the paper the weaker, more general assumption EF = FE is adopted, and the related statistics are examined for different turbulent flows.
15:00 15 mins #153	DISCRETE ADJOINT BASED DATA ASSIMILATION FOR RANS TURBULENCE MODELS Oliver Brenner, Patrick Jenny Abstract: To this day, flow analysis based on the Reynolds-Averaged Navier-Stokes (RANS) equations is popular in industrial applications, not least due to its relatively low computational cost and limitations of turbulence models. Traditional parametric closure models for the Reynolds stresses are for example calibrated by using experimental data or theoretical considerations of canonical flows. Recently, a number of approaches have been presented to increase the predictive capabilities of RANS simulations by data driven turbulence models. In this work, we propose a variational data assimilation method based on the discrete adjoint method [2] to incorporate sparse measurement data into RANS forward simulations of specific set-ups. The goal is to tune the parameters of existing and well accepted turbulence models (e.g. k-epsilon) to flow specific values, such that simulation results better match their respective reference data. The discrete adjoint approach - often used in topology and shape optimization applications - is applied to compute gradients of a cost function that measures the mismatch between forward and reference solution. Subsequently, this information is used in a gradient based optimization procedure. Li et al. [6], for example, have presented a similar approach by computing cost function gradients with respect to the closure model parameters of the k-omega model. Their approach, however, deviates from our method in two key points, namely the computation of the gradient and the definition of the parameters. While they use a finite difference approach, we make use of the discrete adjoint method to evaluate the gradient information. Furthermore, we treat the closure model parameters as spatially variable fields and not as globally valid constants. In this aspect, our approach is similar to the spatially varying term used by Singh and Duraisamy [7]. The number of parameters to be optimized is given by the mesh resolution times the number of model parameters, a possibly large number. By applying the discrete adjoint method the cost of a gradient evaluation is almost independent of the number of parameters. Errors and uncertainties in RANS turbulence models result from different sources, e.g. from model form errors or parameter values. Referring to the four levels of simplification in turbulence modelling described by Duraisamy et al. [3], this work is solely concerned with level L4, i.e. with uncertainties in the model coefficients. An in-house solver implemented with the open-source toolbox OpenFOAM [1] is used to compute the solution to the forward problem and the adjoint gradient. Moreover, the optimization loop is controlled by a Python script, which makes use of SciPy's diverse selection of gradient based optimization algorithms [5]. We demonstrate our method by applying it to simulations of the periodic hills case [4] with the k-epsilon model and various reference data conditions. Due to the considerably higher cost of solving for the adjoint variables in time-dependent cases, the presented work is limited to stationary problems. Furthermore, only the incompressible RANS equations are considered.
15:15 15 mins #38	Can we derive turbulent closure using lattice gas? Vincent Labarre, Bérengère Dubrulle, Didier Paillard Abstract: Most simulations of highly turbulent fluids need a model i.e. a turbulent closure hypothesis. Most models use a parametrization connecting the turbulent fluxes to the gradient of resolved variables. Therefore, this method requires the calibration of free parameters such as turbulent viscosity that depend on the flow condition and reduces the applicability of the models to general or changing conditions. The main difficulty in finding useful closure of turbulent flows is their fundamental non-equilibrium nature and their huge number of degrees of freedom. The framework for general closure models is therefore non-equilibrium statistical physics, which is still a developing area. In this talk, we try to apply recent progress in non-equilibrium statistical physics to investigate the possibility to obtain closure hypothesis in simple models that describe a stationary out of equilibrium flow under a force field (such as Gravity or Coriolis), and a thermodynamic force (gradient of a thermodynamic variable like temperature). For this, we use a simple lattice gas model, the HPP model with a bulk forcing between two reservoirs of different densities. In the hydrodynamic limit, we derive analytically the link between the current of particles and the reservoirs densities and forcing parameter. Our relation is compared with numerical results. The generalization to more isotropic lattices and/or with two populations to take into account thermal effects is discussed.
15:30 15 mins #97	Synchronizing turbulence via nudging Patricio Clark Di Leoni, Andrea Mazzino, Luca Biferale Abstract: Nudging is a data assimilation technique used to control the evolution of a dynamical system. Here we characterize the technique for three-dimensional isotropic turbulent flows, using both data provided in configuration space of in Fourier space. We show that if sufficient data is supplied the nudged turbulent flow can synchronize to the data given (even in points or scales that are not nudged). In other cases, partial synchronization can also be achieved. We also demonstrate how in the presence of large-scale coherent structures, as is the case for rotating turbulent flows, nudging works remarkably better than in the isotropic case. Nudging is thus presented as a tool to probe for the key degrees of freedom in a turbulent field.