Visual Descriptors for Dense Tensor Fields in Computational Turbulent Combustion: A Case Study

Simulation and modeling of turbulent flow, and of turbulent reacting flow in particular, involve solving for and analyzing time-dependent and spatially dense tensor quantities, such as turbulent stress tensors. The interactive visual exploration of these tensor quantities can effectively steer the computational modeling of combustion systems. In this article, the authors analyze the challenges in dense symmetric-tensor visualization as applied to turbulent combustion calculation; most notable among these challenges are the dataset size and density. They analyze, together with domain experts, the feasibility of using several established tensor visualization techniques in this application domain. They further examine and propose visual descriptors for volume rendering of the data. Of these novel descriptors, one is a density-gradient descriptor which results in Schlieren-style images, and another one is a classification descriptor inspired by machine-learning techniques. The result is a hybrid visual analysis tool to be utilized in the debugging, benchmarking and verification of models and solutions in turbulent combustion. The authors demonstrate this analysis tool on two example configurations, report feedback from combustion researchers, and summarize the design lessons learned.  Computational simulation of turbulent combustion for gas turbine design has become increasingly important in the last two decades, due in part to environmental concerns and regulations on toxic emissions. Such modern gas turbine designs feature a variety of mixing fuel compositions and possible flow configurations,1,2 which make non-computational simulations difficult. The focus of the computational research effort in this direction is on the development of computational tools for the modeling and prediction of turbulent combustion flows. Received June 30, 2015; accepted for publication Nov. 4, 2015;  2015.  Song Zhang. 1062-3701/2016/60(1)/010404/11/$25.00 Tensor quantities are common features in these turbulent combustion models. In particular, stress and strain tensors are often correlated to turbulent quantities—which appear unclosed in the mathematical formulation and thus need to be modeled as part of the computational simulation. Visual identification of the characteristics of such tensor quantities can bring significant insights into the computational modeling process. However, these computational tensor fields are very large and spatially dense—a good example of the Big Data revolution across sciences and engineering. Figure 1 shows an example turbulent combustion configuration, featuring a grid size of 106 and 6× 106 particles (shown as spheres); this dataset should be considered in contrast to traditional tensor datasets, which feature grid sizes in the 102 range. At such large scales, typical glyph encodings become cluttered and illegible. Furthermore, combustion experts seldom have an intuitive understanding of the tensor quantities. In this respect, froma tensor visualization perspective, workingwith these datasets poses an array of challenges. Are traditional tensor and flow representations useful in this context? Does increasing the level of complexity or expressiveness of such representations help or hinder? Is interaction speed more important than the benefits gained from complex descriptors? In this article, we address a specific application design problem. In the process of exploring the design space, we also investigate some of the larger visualization questions above, through the opportunity of a case study in the computational-combustion domain. In thiswork,motivated by an ongoing collaborationwith domain experts,3 we investigate the challenges associated with the exploratory visualization of tensor quantities in turbulent combustion simulations. We first provide a characterization of the problem domain, including a data analysis. Through a case study involving five senior combustion researchers, we then iteratively explore the space of tensor visual encodings. We implement and evaluate several  Marai et al.: Visual descriptors for dense tensor fields in computational turbulent combustion: a case study Figure 1. One timestep in an example turbulent combustion configuration. The grid size is 106. In this image, 6× 106 particles are shown as spheres. This dataset should be contrasted to traditional tensor datasets, which feature sparse grids in the 102 range. At this scale, typical glyph encodings become cluttered. approaches advocated by the visualization community in an interactive prototype, and we contrast these approaches with the best-of-breed visualization practices in the target domain. Based on domain expert feedback, we then focus our efforts on identifying effective visual descriptors for volume rendering of the combustion tensor data. Our contributions include a novel density-gradient descriptor and the adaptation of a machine-learning classification technique. Next, we evaluate the visual descriptors on two computational-combustion datasets of particular interest, and we show the importance of the proposed approach for debugging the numerical simulation of complex configurations. In an effort to better bridge the gap between the combustion and tensor visualization communities, we describe these tensor field datasets. Last but not least, we contribute a summary of design lessons learned from the study and from the application design process. To the best of our knowledge, this is the first formal, exploratory case study of tensor visualization techniques in the context of very large, high-density turbulent combustion flow.  A sufficiently accurate, flexible and reliable model can be used for an in silico combustor rig test as a much cheaper alternative to the reallife rig tests employed in combustor design and optimization. In order to achieve such amodel, themethodology should be well tested and proven with lab-scale configurations. Multiple numerical approaches exist for the generation of such computational models of combustion, most notably Direct numerical simulation (DNS), Reynolds-averaged Navier–Stokes (RANS) and Large eddy simulation (LES). DNS, RANS and LES have complementary strengths. However, allmodels begin by describing the compressible reacting flow via a set of partial differential equations (PDEs) that represent the conservation of mass, momentum and energy. These PDEs are a fully coupled set of multi-dimensional non-linear equations and can be posed in a variety of forms depending on the flow conditions (compressibility, scale, flow regime, etc.).4 In this article, we exemplify the visualization of stress/strain tensors, and therefore restrict the presentation to the pertinent subset of these PDEs, namely the momentum transport equation. Stress, Strain and Turbulent Stress Tensors. A tensor is an extension of the concept of a scalar and a vector to higher orders. For example, while a stress vector is the force acting on a given unit surface, a stress tensor is defined as the components of stress vectors acting on each coordinate surface; thus, stress can be described by a symmetric second-order tensor (a matrix). The velocity stress and strain tensor fields aremanifested in the transport of fluid momentum, which is a vector quantity governed by the following conservation equation: