The exergy concept and compressible turbulence

Turbulence models facilitated by Kolmogorov’s theory play an important role for compressible flows. Typically the basis of these models is the power spectrum of the velocity \({\mathbf {u}}\) or of the density-weighted velocity \({\mathbf {w}}\equiv \rho ^{1/3}{\mathbf {u}}\). While for incompressible flow the quantity turbulent kinetic energy characterises turbulent motions, from the thermodynamic point of view, due to fluctuations of the density and the temperature other kinds of energies play a role at the different scales in compressible turbulence. We generalise the power spectrum of the velocity \({\mathbf {u}}\) from incompressible flows to compressible flows by introducing the exergy spectrum as an application of the exergy concept. Furthermore, we discuss the application of the concept of turbulent exergy to turbulence modelling and demonstrate this approach with a direct numerical simulation and a Large-Eddy-Simulation of homogeneous isotropic turbulence. The advantage of turbulence modelling based on turbulent exergy is shown on the example of the Approximate Deconvolution Model (ADM) where, at smallest scales for its newly introduced entropy formulation, more available energy is extracted from the flow, and this occurs in a more physical way than for the classical equation set of the model using the total energy.