Modeling of Turbulent Flow over 2D Backward-Facing Step Using Generalized Hydrodynamic Equations

The Generalized Hydrodynamic Equations are being investigated for simulating turbulent flows. They were derived from the Generalized Boltzmann Equation by Alexeev (1994), which itself was obtained from first principles via a chain of Bogolubov kinetic equations and considers particles of finite dimensions. Compared to the Navier-Stokes equations, the Generalized Hydrodynamic Equations include new terms representing temporal and spatial fluctuations. These terms introduce a timescale multiplier denoted by \(\tau \) , and the Generalized Hydrodynamic Equations reduce to the Navier-Stokes equations when \(\tau \) equals zero. The nondimensional \(\tau \) is calculated as the product of the Reynolds number and the squared ratio of length scales, \(\tau = Re \times (l/L)^2\) , where l represents the apparent Kolmogorov length scale and L denotes a hydrodynamic length scale. In this study, 2D turbulent flow over a Backward-Facing Step (BFS) with a step height of H = L/3 (where L is the channel height) at Reynolds number Re = 132000 was investigated using finite-element solutions of the GHE. The results were compared to Direct Numerical Simulations (DNS) utilizing the Navier-Stokes equations, and to a \(k-\varepsilon \) turbulence model, as well as experimental data. The comparison encompassed velocity profiles, recirculation zone length, and the velocity flow field. The obtained data confirm that the GHE results are in good agreement with the experimental findings, while other approaches diverge significantly from the experimental data.