Optimal Nonlinear Eddy Viscosity in Galerkin Models of Turbulent Flows

We propose a variational approach to identification of an optimal nonlinear eddy viscosity as a subscale turbulence representation for POD models. The ansatz for the eddy viscosity is given in terms of an arbitrary function of the resolved fluctuation energy. This function is found as a minimizer of a cost functional measuring the difference between the target data coming from a resolved direct or large-eddy simulation of the flow and its reconstruction based on the POD model. The optimization is performed with a data-assimilation approach generalizing the 4D-VAR method. POD models with optimal eddy viscosities are presented for a 2D incompressible mixing layer at $Re=500$ (based on the initial vorticity thickness and the velocity of the high-speed stream) and a 3D Ahmed body wake at $Re=300,000$ (based on the body height and the free-stream velocity). The variational optimization formulation elucidates a number of interesting physical insights concerning the eddy-viscosity ansatz used. The 20-dimensional model of the mixing-layer reveals a negative eddy-viscosity regime at low fluctuation levels which improves the transient times towards the attractor. The 100-dimensional wake model yields more accurate energy distributions as compared to the nonlinear modal eddy-viscosity benchmark {proposed recently} by \"Osth et al. (2014). Our methodology can be applied to construct quite arbitrary closure relations and, more generally, constitutive relations optimizing statistical properties of a broad class of reduced-order models.Comment: 41 pages, 16 figures; accepted for publication in Journal of Fluid Mechanic

The flow around a simplified tractor-trailer model studied by large eddy simulation

Large-eddy simulation (LES) is used to study the flow around a simplified tractor-trailer model. The model consists of two boxes placed in tandem. The front box represents the cab of a tractor-trailer road vehicle and the rear box represents the trailer. The LES was made at the Reynolds number of 0.51×106 based on the height of the rear box and the inlet air velocity. Two variants of the model were studied, one where the leading edges on the front box are sharp and one where the edges are rounded. One small and one large gap width between the two boxes were studied for both variants. Two computational grids were used in the LES simulations and a comparison was made with available experimental force measurements. The results of the LES simulations were used to analyze the flow field around the cab and in the gap between the two boxes of the tractor-trailer model. Large vortical structures around the front box and in the gap were identified. The flow field analysis showed how these large vortical structures are responsible for the difference in the drag force for the model that arises when the leading edges on the front box are rounded and the gap width is varied

Simulations of flow around a simplified train model with a drag reducing device

Partially Averaged Navier Stokes is used to simulate the flow around a simple train model. The train model has previously been studied in wind tunnel experiments and has a length to height/width ratio of 7:1. The Reynolds number based on the height of the train model is 0.37 x 10^6. For this Reynolds number, the flow separates from the curved leading edges on the front then attaches again on the roof and sides forming a boundary layer there before separating in the wake. The first case is of the natural flow around the train model where direct comparison to experimental data of drag coefficient and pressure coefficient are made. In the second case an open cavity is placed on the base of the train model with the aim of reducing the overall drag on the model. The results show that the drag for model with the cavity is reduced by some 10% compared to the drag of the natural case. The agreement to experimental data for the natural case is not perfect but the general features in the flow field are simulated correctly

On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body

We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to Large Eddy Simulation data for a flow around the vehicle-like bluff body call Ahmed body. This flow has three challenges for any reduced-order model: a high Reynolds number, coherent structures with broadband frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin models are found to be most accurate with modal eddy viscosities as proposed by Rempfer & Fasel (1994). Robustness of the model solution with respect to initial conditions, eddy viscosity values and model order is only achieved for state-dependent eddy viscosities as proposed by Noack, Morzynski & Tadmor (2011). Only the POD system with state-dependent modal eddy viscosities can address all challenges of the flow characteristics. All parameters are analytically derived from the Navier-Stokes based balance equations with the available data. We arrive at simple general guidelines for robust and accurate POD models which can be expected to hold for a large class of turbulent flows.Comment: Submitted to the Journal of Fluid Mechanic

Cluster-based reduced-order modelling of a mixing layer

We propose a novel cluster-based reduced-order modelling (CROM) strategy of unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt et al. 2006) and and transition matrix models introduced in fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a potential alternative to POD models and generalises the Ulam-Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron-Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Secondly, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e.g. using finite-time Lyapunov exponent and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.Comment: 48 pages, 30 figures. Revised version with additional material. Accepted for publication in Journal of Fluid Mechanic

Active flow control for drag reduction of vehicles using large eddy simulation, experimental investigations and reduced-order modeling

The purpose of this short paper is to introduce first results obtained in a collaborative research between the partners. This research is dedicated to drag reduction of vehicles using LES, experimental investigation and ultimately reduced order modeling. First numerical and experimental results are presented. Experiments show that periodic forcing at high frequencies and amplitudes of the order of the upstream velocities can be viewed as a promising strategy for drag reduction targeted control of three-dimensional bluff-bodies

"Outroduction":A research agenda on collegiality in university settings

Collegiality is the modus operandi of universities. Collegiality is central to academic freedom and scientific quality. In this way, collegiality also contributes to the good functioning of universities’ contribution to society and democracy. In this concluding paper of the special issue on collegiality, we summarize the main findings and takeaways from our collective studies. We summarize the main challenges and contestations to collegiality and to universities, but also document lines of resistance, activation, and maintenance. We depict varieties of collegiality and conclude by emphasizing that future research needs to be based on an appreciation of this variation. We argue that it is essential to incorporate such a variation-sensitive perspective into discussions on academic freedom and scientific quality and highlight themes surfaced by the different studies that remain under-explored in extant literature: institutional trust, field-level studies of collegiality, and collegiality and communication. Finally, we offer some remarks on methodological and theoretical implications of this research and conclude by summarizing our research agenda in a list of themes

A LES Study of a Simplified Tractor-Trailer Model

A numerical study using large eddy simulation (LES) of the flow around a simplified tractor-trailer model has been done. The model is that from the experimental investigation [1] and consists of two boxes placed in tandem arrangement. The Reynolds number based on the height of the rear box and free stream velocity is 0.51 x 106. The first box has normalized height, width and depth of 0.92, 0.92 and 0.67, respectively, and represents the cab of a truck. The second box has height, width and depth of 1, 1, and 2.5, respectively, and represents the load of a truck. The front box is lifted 0.21 above the simulated moving ground and the rear box is lifted 0.5. The aim of the present study has been to investigate the influence of the size of the gap between the tractor and the trailer on the flow physics and the resulting aerodynamic performance of the tractor-trailer model. Two different models have been investigated. One model with sharp front edges of the front box and one with rounded front edges of the front box. Experimental results [1] have shown that the two cases exhibit large differences in the drag coefficient depending on the gap width between the boxes. For smaller gap widths, the model with rounded front edges has a considerably smaller drag, while for larger but still practical gap widths the drag exceeds that of the sharp-edged model significantly. Simulations with three different gap widths for each model has been simulated using LES. The results has shown good agreement with the available experimental data from [1] for the sharp model but less accurate results for the rounded model even though the general trend is in agreement. The mean velocity field has been analysed and the flow physics responsible for the difference in drag for the models has been found

A study of the aerodynamics of a generic container freight wagon using Large-Eddy Simulation

In this work simulations using the Large Eddy Simulation technique have been made of the flow around a generic container freight wagon model. The model consists of one 11.8 m standard length container placed on a wagon. Details of the undercarriage such as wheels are included, but the container is generic and smoothed in comparison to a real freight wagon. The Reynolds number of the flow is 105 based on the container width of 2.354 m. Two cases have been considered in the study, one case where the wagon is standing alone and one case where it is submerged into a train set with wagons ahead and behind the wagon. The latter case is simulated using periodic boundary condition. Both the time-averaged and the instantaneous flow around the wagon for the two cases are described. For the single wagon case, it is found that the separation bubble formed on the roof of the container oscillates back and forth in the streamwise direction and that this oscillation is in phase with oscillations found in the upper shear layer of the ring vortex in the wake. The mechanism that is causing the synchronization of the oscillations of the separation bubble at the front and the upper shear layers in the wake is found to be waves of vorticity being shed from the separation bubble. The time-averaged ring vortex in the near wake of the single wagon is found to be inclined due to the disturbance of the undercarriage details on flow in the lower shear layer. The lower center of the ring vortex is located closer to the base face than the upper center. The drag coefficient of the wagon in the periodic case was found to be only 10% of that of the single wagon case. This is due to two symmetrical counter-rotating vortices found in the gaps which make the train set appear as a single body to the oncoming flow and shielding the wagon from any direct impingement of the flow. The counter-rotating vortices in the gap are found to inhibit periodic oscillations in the lateral direction. These oscillations cause vortical structures to form by the air that is pushed out from the gap and these flow structures cause a dominating oscillation of non-dimensional frequency St=0.12 in the side force signal