Higher-Order Correlations Between Thermodynamic Fluctuations in Compressible Aerodynamic Turbulence
Georges A. Gerolymos, Isabelle Vallet
TL;DR
This paper explores how thermodynamic variables like pressure, density, and temperature fluctuate in turbulent flows, focusing on higher-order correlations and nonlinear effects.
Contribution
The study derives exact equations for higher-order correlations and validates them using direct numerical simulations of compressible turbulence.
Findings
Nonlinear terms from density-temperature fluctuations significantly affect third-order correlations.
Exact equations linking third-order moments are validated using DNS data for compressible turbulent flows.
Linearized relations help identify independent moment 4-tuples for further analysis.
Abstract
This paper studies the exact and approximate relations between fluctuations in thermodynamic variables (pressure, density and temperature) that are imposed by the dilute-gas (Z=1) equation-of-state (EoS), which is a satisfactory approximation of air thermodynamics for a wide range of pressures and temperatures. It focuses on triple- and higher-order correlations, extending previous studies that concentrated on second-order moments, with emphasis on the mathematical relations, which are generally valid independently of the particular flow configuration. Exact equations are developed both involving only single-variable moments and relating the correlations between variables. These contain nonlinear terms generated by the density-temperature fluctuation product in the fluctuating EoS. The importance of the nonlinear terms in the 6 exact equations between the 10 third-order moments is…
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Taxonomy
TopicsCombustion and flame dynamics · Computational Fluid Dynamics and Aerodynamics · Gas Dynamics and Kinetic Theory