Numerical Benchmark for High-Reynolds-Number Supercritical Flows with Large Density Gradients

Because of the extreme complexity of physical phenomena at high pressure, only limited data are available for solver validation at device-relevant conditions such as liquid rocket engines, gas turbines, or diesel engines. In the present study, a two-dimensional direct numerical simulation is used to establish a benchmark for supercritical flow at a high Reynolds number and high-density ratio at conditions typically encountered in liquid rocket engines. Emphasis has been placed on maintaining the flow characteristics of actual systems with simple boundary conditions, grid spacing, and geometry. Results from two different state-of-the-art codes, with markedly different numerical formalisms, are compared using this benchmark. The strong similarity between the two numerical predictions lends confidence to the physical accuracy of the results. The established database can be used for solver benchmarking and model development at conditions relevant to many propulsion and power systems

From Empirics to Empiricists

Although the notion of empiricism looms large in many histories of early modern philosophy, its origins are not well understood. This paper aims to shed light on them. It examines the notions of empirical philosopher, physician, and politician that are employed in a range of seventeenth- and eighteenth-century texts, alongside related notions (e.g. "experimental philosophy") and methodological stances. It concludes that the notion of empiricism used in many histories of early modern thought does not have pre-Kantian origins. It first appeared and became widely used in late eighteenth-century Germany, in the course of the early debates on Kant's Critical philosophy