Andrea Gruber

Reduced aliasing formulations of the convective terms within the Navier-Stokes equations for a compressible fluid

The effect on aliasing errors of different formulations describing the cubically nonlinear convective terms within the discretized Navier-Stokes equations is examined in the presence of a non-trivial density spectrum. Fourier analysis shows that the existing skew-symmetric forms of the convective term result in reduced aliasing errors relative to the conservation form. Several formulations of the convective term, including a new formulation proposed for cubically nonlinear terms, are tested in direct numerical simulation (DNS) of decaying compressible isotropic turbulence both in chemically inert (small density fluctuations) and reactive cases (large density fluctuations) and for different degrees of resolution. In the DNS of reactive turbulent flow, the new cubic skew-symmetric form gives the most accurate results, consistent with the spectral error analysis, and at the lowest cost. In marginally resolved DNS and LES (poorly resolved by definition) the new cubic skew-symmetric form represents a robust convective formulation which minimizes both aliasing and computational cost while also allowing a reduction in the use of computationally expensive high-order dissipative filters.

Turbulent flame–wall interaction: a direct numerical simulation study

A turbulent flame-wall interaction (FWI) configuration is studied using three-dimensional direct numerical simulation (DNS) and detailed chemical kinetics. The simulations are used to investigate the effects of the wall turbulent boundary layer (i) on the structure of a hydrogen-air premixed flame, (ii) on its near-wall propagation characteristics and (iii) on the spatial and temporal patterns of the convective wall heat flux. Results show that the local flame thickness and propagation speed vary between the core flow and the boundary layer, resulting in a regime change from flamelet near the channel centreline to a thickened flame at the wall. This finding has strong implications for the modelling of turbulent combustion using Reynolds-averaged Navier-Stokes or large-eddy simulation techniques. Moreover, the DNS results suggest that the near-wall coherent turbulent structures play an important role on the convective wall heat transfer by pushing the hot reactive zone towards the cold solid surface. At the wall, exothermic radical recombination reactions become important, and are responsible for approximately 70 % of the overall heat release rate at the wall. Spectral analysis of the convective wall heat flux provides an unambiguous picture of its spatial and temporal patterns, previously unobserved, that is directly related to the spatial and temporal characteristic scalings of the coherent near-wall turbulent structures.

Computation of three-dimensional three-phase flow of carbon dioxide using a high-order WENO scheme

Abstract We have developed a high-order numerical method for the 3D simulation of viscous and inviscid multiphase flow described by a homogeneous equilibrium model and a general equation of state. Here we focus on single-phase, two-phase (gas–liquid or gas–solid) and three-phase (gas–liquid–solid) flow of CO 2 whose thermodynamic properties are calculated using the Span–Wagner reference equation of state. The governing equations are spatially discretized on a uniform Cartesian grid using the finite-volume method with a fifth-order weighted essentially non-oscillatory (WENO) scheme and the robust first-order centered (FORCE) flux. The solution is integrated in time using a third-order strong-stability-preserving Runge–Kutta method. We demonstrate close to fifth-order convergence for advection–diffusion and for smooth single- and two-phase flows. Quantitative agreement with experimental data is obtained for a direct numerical simulation of an air jet flowing from a rectangular nozzle. Quantitative agreement is also obtained for the shape and dimensions of the barrel shock in two highly underexpanded CO 2 jets.

Turbulence combustion closure model based on the Eddy dissipation concept for large eddy simulation

Modeling of turbulence-chemistry interaction is still a challenge. Turbulence modeling with Large Eddy Simulation (LES) has been matured enough for industrial problems. In LES eddies up to the filter width are resolved on the grid scales, but the fine structures where combustion takes place are still not resolved, which calls for combustion modeling in LES. Combustion closure in LES is achieved througha TurbulenceChemistry InteractionModel (TCIM). Most of the developed TCIM are based on the already existing RANS model. In the present study, a TCIM based on the Eddy Dissipation Concept (EDC) is proposed for large eddy simulation. The model is formulated from subgrid viscosity and filtered strain rate tensor. EDC model constants are modified to account for the partial energy cascading in LES. The other model used in this study is the steady state Flamelet model. Another issue with reacting flows is the solution of the pressure correction Poisson’s equation with density time derivative term, which causes severe time constraint per iteration. Density time derivative is the most destabilizing part of the calculation when the density from equation of state is used. In the present study density is formulated from species mass fraction, which is numerically stable and computationally less expensive. LES of the H2/N2 “FlameH3” non-premixedunconfined turbulent jet flame is performed using LESEDC and Flamelet model. The Reynolds number based on nozzle diameter and jet bulk velocity is 10,000. The chemistry used for LES-EDC model is a fastchemistry. Results of the simulations in the form of means and variances of