Development and validation of Navier–Stokes characteristic boundary conditions applied to turbomachinery simulations using the lattice Boltzmann method

Abstract

This article reports a procedure to implement as well as to validate non-reflecting boundary conditions applied for turbomachinery simulations, using Navier-Stokes characteristic boundary conditions in a compressible lattice Boltzmann solver. The implementation of both an inlet condition imposing total pressure, total temperature, and flow angles, as well as an outlet condition imposing a static pressure profile that allows the simulation to reach a simplified radial equilibrium, is described within the context of a lattice Boltzmann approach. The treatment at the boundaries relies on the characteristic methodology to derive conditions which are non-reflecting in terms of acoustics and is also compatible with turbulence injection at the inlet. These properties are evaluated on test cases of increasing complexity, ranging from a simple 2D periodic domain to an S-duct stage with turbulence injection.

Inter-Compressor Annular S-duct Simulations using the Lattice Boltzmann Method

“…At the inlet, an azimuthal averaging of the experimental data is performed to impose radial profiles of total pressure, total temperature and flow angles using a LODI formulation Gianoli et al (2022). Moreover, turbulence injection is set at the inlet with an intensity of 5% and a turbulent length scale l = H in /5 corresponding to the experimental measurements.…”

“…At the outlet, uniform static pressure is taken from the experimental data and will be dynamically adjusted to match the correct mass flow Duchaine & Gicquel (2019). The outlet condition uses a LODI formalism that naturally respects the radial equilibrium assumption Gianoli et al (2022). Concerning the rest of the boundaries, adiabatic walls are imposed in association with a wall law.…”

Characteristic Boundary Condition for Thermal Lattice Boltzmann Methods

“…Few implementations of characteristic boundary conditions for isothermal (single-speed) LBM have been reported in the literature [24,25,26,27], finding application in the simulation of fluid flows in high Reynolds number regimes [28,29,30]. To the best of our knowledge, there are currently only two works in the literature where the application of characteristic BCs for multi-speed LBM is discussed: the CBC for the Navier-Stokes equations presented in [24] has been used in conjunction with multi-speed velocity stencils in a previous article [31] by the authors of the work at hand, and recently multi-speed CBC was used in the context of thermo-acoustic problems governed by the Euler equations [32].…”