The characterisation of small-scale turbulence has been an active area of research for decades and this includes, particularly, the analysis of small-scale isotropy, as postulated by Kolmogorov. In particular, the question if the dissipation tensor is isotropic or not, and how it is related to the anisotropy of the Reynolds stresses is of particular interest for modelling purposes. While this subject has been extensively studied in the context of isothermal flows, the situation is more complicated in turbulent reacting flows because of heat release. Furthermore, the landscape of Computational Fluid Dynamics is characterised by a multitude of methods ranging from Reynolds-averaged to Large Eddy Simulation techniques, and they address different ranges of scales of the turbulence kinetic energy spectrum. Therefore, a multiscale analysis of the anisotropies of Reynolds stress, dissipation and sub-grid scale tensor has been performed by using a DNS database of statistically planar turbulent premixed flames. Results show that the coupling between dissipation tensor and Reynolds stress tensor is weaker compared to isothermal turbulent boundary layer flows. In particular, for low and moderate turbulence intensities, heat release induces pronounced anisotropies which affect not only fluctuation strengths but also the characteristic size of structures associated with different velocity components.

We further elaborate on the generalized formulation for cubic equation of state proposed by Cismondi and Mollerup [Fluid Phase Equilib. 232, 74–89 (2005)]. With this formulation, all well-known cubic equations of state can be described with a certain pair of values, which allow for a generic implementation of different equations of state. Based on this generalized formulation, we derive a complete thermodynamic model for computational fluid dynamics simulations by providing the resulting correlations for all required thermodynamic properties. For the transport properties, we employ the Chung correlations. Our generic implementation includes the often used equations of state Soave–Redlich–Kwong and Peng–Robinson and the Redlich–Kwong–Peng–Robinson equation of state. The first two assume a universal critical compressibility factor and are, therefore, only suitable for fluids with a matching critical compressibility. The Redlich–Kwong–Peng–Robinson overcomes this limitation by considering the equation of state parameter as a function of the critical compressibility. We compare the resulting thermodynamic modeling for the three equations of state for selected fluids with each other and CoolProp reference data. Additionally, we provide a Python tool called real gas thermodynamic python library (realtpl). This tool can be used to evaluate and compare the results for a wide range of different fluids. We also provide an implementation of the generalized form in OpenFOAM.

No abstract