Development of a Projection-Based Method for the Numerical Calculation of Compressible Reactive Flows

Abstract

The ability to calculate compressible reactive flows enables the computation of thermoacoustic interactions in gas turbine combustor systems. A new projection-based numerical method able to compute compressible reactive flows is developed within this work. This computational scheme is based on a modified Helmholtz decomposition, by which an arbitrary vector field is split up into a field with a so-called divergence constraint and an irrotational field. This leads to a fractional step scheme which consists of a predictor and a corrector step. The Poisson equation solved for the pressure in case of incompressible flows is extended to a Helmholtz equation for the computation of compressible flows. After solving the corrector step, the mass and momentum balances are fulfilled. This results in a fast numerical scheme, since no further iterations need to be computed. Based on the modified Helmholtz decomposition, it is shown that the created method can be understood as an extension of the incompressible projection scheme. Moreover, the spatial and temporal order of accuracy of incompressible projection-based methods are discussed and the ones of the compressible scheme are determined. The created compressible projection-based method is further on validated against a one-dimensional linear acoustic test case from the literature, whereby an analytical solution can be derived.

Stochastic and Direct Combustion Noise Simulation of a Gas Turbine Model Combustor

“…Results of combustion noise simulation is not only validated with experimental data, but also evaluated against a direct, compressible method. Therefore, the Compressible Projection Method from Reichling et al [39] is taken into consideration. This approach extends the incompressible, pressure-based solver of the unstructured finite volume based CFD code THETA [10,39] for the treatment of weakly compressible flows.…”

“…Therefore, the Compressible Projection Method from Reichling et al [39] is taken into consideration. This approach extends the incompressible, pressure-based solver of the unstructured finite volume based CFD code THETA [10,39] for the treatment of weakly compressible flows. It was developed based on projection schemes from Chorin [7] and Temam [47].…”

“…(38), the indicator ϕ in Eqn. (39) represents a discrete form of the combustion noise source term for vanishing spatial and temporal separation. Or, in other words, it indicates regions in the combustion chamber where combustion noise sources according to Eqn.…”

Direct Combustion Noise Simulation of a Lean Premixed Swirl Flame using Stochastic Sound Sources

“…34,35,36 The code was originally designed for the simulation of steady and unsteady turbulent reacting flows with an incompressible solver on unstructured meshes using a dualgrid approach. However, in latest works it was extended by pressure based compressible solver approaches 37,38,34,35,36 in order to be able to properly capture acoustics and thermoacoustic phenomena as well as compressible flow regimes. Therefore, partially scale resolving simulations with THETA serve as comparison cases for the herein carried out simulations with the hybrid approach FRPM-CN in terms of computational turnaround times.…”

“…The simulations are conducted with the finite volume based DLR inhouse code THETA. 59,34 The reacting CFD RANS calculations are based on an incompressible formulation of the basic Eqs. static pressure is set to ambient reference conditions.…”