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.