Large Eddy Simulation of a Gas Turbine Combustion Chamber

An industrial gas turbine burner operating at a pressure of 3 bar is simulated using the sgs-pdf evolution equation approach in conjunction with the Eulerian stochastic field solution method in the context of Large Eddy Simulation. A dynamic version of the Smagorinsky model is adopted for the sub-grid stresses and eight stochastic fields were utilised to characterize the influence of the sub-grid fluctuations. The chemistry was represented by an ARM reduced GRI 3.0 mechanism with 15 reaction steps and 19 species. The results show good agreement with the experimental data in the flame region at different axial locations. The results serve to demonstrate that simulations of complex combustion problems in industrial geometries are achievable. Introduction The turbulent premixed flames to be found in industrial gas turbine combustors are difficult to study due to high levels turbulence, fast chemistry and complex geometrical features. Most of these devices operate at high pressure, which adds to the difficulty of obtaining experimental data and accounting for pressure effects in computational models. Large Eddy Simulation (LES) is a powerful and promising modelling technique particularly for highly swirling and unsteady flows. In case of LES of turbulent combustion, account must be taken of the interactions between turbulence and chemical reaction. The main difficulties encountered in achieving this arise from the filtered chemical source terms, which represents the net rate of species formation and consumption through chemical reaction. Since these reactions are highly non-linear, the filtered values of the fields of chemical species mass fraction and temperature are strongly influenced by the sub-grid scale (sgs) fluctuations of the reactants and the temperature. A method of accounting for these is from the joint scalar probability density function (pdf ) of all the relevant scalar quantities which provides all the necessary information required to evaluate the filtered chemical source terms. The modelled form of the equation governing the time evolution of the joint pdf of the complete set of scalars provides a means of determining all of the time and spatially varying one-point statistics. The chemical source terms appear in closed form in this equation and no further modelling is required, beyond specification of a chemical reaction mechanism. Due to the high dimensionality of the pdf evolution equation, a solution only becomes feasible if stochastic methods are applied. Conventionally Lagrangian stochastic particle methods have been adopted for the pdf equation in conjunction with an Eulerian formulation for the velocity and pressure fields. Alternatively, Eulerian approaches have been formulated (see [1] and [2]). These methods introduce stochastic fields, which form a system of stochastic partial differential equations having the same one-point moments as the modelled pdf evolution equation, e.g. [3]. A main advantage of the latter method is that the solutions give rise to fields that are continuous and differentiable in space and which are thus free of spatially varying stochastic errors. Main Objectives The LES-pdf formulation in conjunction with the Eulerian stochastic field solution method has been successfully applied in a range of burning configurations: ignition [4, 5] and autoignition [6], [7], non-premixed [8] and premixed regimes [9]. The majority of cases were at atmospheric pressure and in relatively simple geometrical configurations. This paper aims to validate the LES-pdf method for an industrial gas turbine burner (Siemens SGT-100), 1 MW thermal power operating at a pressure of 3 bar. Although the geometrical features of the burner were retained, the operating conditions (pressure, temperature and mixture fractions) studied and discussed in this paper differ from those of the burner in SGT-100 gas turbine. The burner, (a) Experimental setup (b) Computational Domain Figure 1: Siemens SGT-100 burner, experimental setup and computational domain. shown in Fig. (1a), was studied experimentally in the high pressure rig facility of the German Aerospace Center (DLR) Stuttgart, Germany [10], [11]. For ease of optical access the combustion chamber was modified so that its cross-section was square. Planar Induced Velocimetry (PIV), 1D Raman and OH PLIF data were collected from the burner. The computational domain used for LES is shown in Fig. (1b) Large Eddy Simulation LES involves a direct numerical simulation of the large scale energetic motions with the effects of the unresolved sub-grid scale motions being modelled. The separation of the scales is achieved through a spatial filter, which for a function f = f(x, t) is defined as its convolution with a filter function G according to: f(x, t) = ∫ Ω G(x− x′; ∆(x))f(x′, t)dx′ (1) The integration is defined over the entire flow domain Ω and the filter function has a characteristic width of ∆, which may vary with position. In combusting flows, strong density fluctuations occur which can be treated through the use of a density weighted filter, defined by f(x, t) = ρf/ρ. Applying a density weighted filter to the Continuity and Navier-Stokes equation leads to the following set of filtered equations: Continuity: ∂ρ ∂t + ∂ρũi ∂xi = 0, (2) Momentum: ∂ρũi ∂t + ∂ρũiũj ∂xj = − ∂p ∂xi + ∂ ∂xj σij − ∂ ∂xj τij (3)