Large Eddy simulation of supersonic combustion using a probability density function method

The scramjet propulsion system is regarded to be a key technology to deliver the next generation of hypersonic planes. It consists of a ramjet engine in which the combustion occurs at supersonic speed. Experiments have been used to investigate the scramjet engine, however, the high costs of gathering data is a limiting factor in its development. In this context, the numerical simulation is an affordable alternative to shed a light into supersonic combustion. The simulation of high-speed compressible and reactive flows, however, is not straightforward, including shock/boundary layer interactions and combustion. Nonetheless, most combustion models have been designed for subsonic flames and their portability to high-speed flows is non-trivial. This work investigates the use of the Probability Density Function (PDF) method for supersonic combustion within the Large Eddy Simulation (LES) framework. Two methods are considered: one is an extension of a joint scalar PDF model (SPDF) for high speed flows and the other is a new joint velocity-scalar PDF formulation (VSPDF). The LES-PDF equations are solved using the Eulerian stochastic fields method, which is implemented into the in-house compressible code CompReal. Their performance are evaluated through a reactive shock-tube, mixing layers and a homogeneous isotropic turbulence cube simulation. Two supersonic burner configurations are simulated to validate the code against experimental data. The results show that sub-grid contributions are important at coarse meshes and the stochastic fields approach can reproduce experimental results. The University of Virginia scramjet configuration A is also simulated using the joint scalar PDF model. Results of topwall pressure, temperature and molar fractions are compared with experimental data. Overall, the results suggest that the joint scalar PDF is the most robust and reliable formulation and the sub-grid closures for the joint velocity-scalar PDF require further investigation.Open Acces

Dynamic localized turbulent diffusion and its impact on the galactic ecosystem

Modelling the turbulent diffusion of thermal energy, momentum, and metals is required in all galaxy evolution simulations due to the ubiquity of turbulence in galactic environments. The most commonly employed diffusion model, the Smagorinsky model, is known to be overdiffusive due to its strong dependence on the fluid velocity shear. We present a method for dynamically calculating a more accurate, locally appropriate, turbulent diffusivity: the dynamic localized Smagorinsky model. We investigate a set of standard astrophysically relevant hydrodynamical tests, and demonstrate that the dynamic model curbs overdiffusion in non-turbulent shear flows and improves the density contrast in our driven turbulence experiments. In galactic discs, we find that the dynamic model maintains the stability of the disc by preventing excessive angular momentum transport, and increases the metal-mixing time-scale in the interstellar medium. In both our isolated Milky Way-like galaxies and cosmological simulations, we find that the interstellar and circumgalactic media are particularly sensitive to the treatment of turbulent diffusion. We also examined the global gas enrichment fractions in our cosmological simulations, to gauge the potential effect on the formation sites and population statistics of Population III stars and supermassive black holes, since they are theorized to be sensitive to the metallicity of the gas out of which they form. The dynamic model is, however, not for galaxy evolution studies only. It can be applied to all astrophysical hydrodynamics simulations, including those modelling stellar interiors, planetary formation, and star formation

Presumed and transported PDF methods applied to turbulent premixed flames

The current study focuses on the modelling of turbulent premixed or partially premixed flames over a wide range of combustion regimes using various fuels. Opposed flows featuring fractal-generated turbulence are examined using different classes of models. The reacting case is in the flamelet regime of combustion and two-scalar joint β -bimodal presumed PDF and transported PDF approaches are applied for scalar statistics. In the isothermal case the k − ε model works comparatively well, in contrast to previous studies, while in the reacting case the second moment closures are outperforming the eddy viscosity based closures. The transported PDF approach indicates an under-prediction of the turbulent burning velocity in this flow. The latter approach is therefore applied to compute freely propagating turbulent premixed flames using comprehensive chemistry. Turbulent burning velocities are extracted and compared with experimental data. The computed cases are covering the laminar flamelet to the distributed reaction zone regime. The mixture reactivity is also varied through different fuel/air mixtures and explored in terms of the Zeldovich number. The fuel/air composition studied include fuel-lean CH4, stoichiometric CH4 and C2H6 and fuel-rich H2 mixtures. The impact of molecular transport is investigated through the inclusion of an explicit analytical formulation. A multi-scale scalar dissipation rate closure that accounts for the influence of the Da number is extended in a simple manner to include Le number effects. An industrial swirl-stabilised partially premixed fuel-rich CH4 flame is simulated at realistic gas turbine conditions using the node-based Eulerian transported PDF approach coupled with a second moment closure for the velocity field. The case is in the well stirred reactor regime and the chemical kinetics is modelled using a global reaction scheme for hydrocarbon combustion. The flow field is initialised and compared with the predictions of the two-scalar joint β-bimodal presumed PDF approach

VS-FMDF and EPVS-FMDF for Large Eddy Simulation of Turbulent Flows

The first part of this dissertation is concerned with implementation of the joint ``velocity-scalar filtered mass density function'' (VS-FMDF) methodology for large eddy simulation (LES) of Sandia Flame D. This is a turbulent piloted nonpremixed methane jet flame. In VS-FMDF, the effects of the subgrid scale chemical reaction and convection appear in closed forms. The modeled transport equation for the VS-FMDF is solved by a hybrid finite-difference/Monte Carlo scheme. For this flame (which exhibits little local extinction), a flamelet model is employed to relate the instantaneous composition to the mixture fraction. The LES predictions are compared with experimental data. It is shown that the methodology captures important features of the flame as observed experimentally. In the second part of this dissertation, the joint ``energy-pressure-velocity-scalar filtered mass density function'' (EPVS-FMDF) is developed as a new subgrid scale (SGS) model for LES of high-speed turbulent flows. In this model, the effects of compressibility are taken into account by including two additional thermodynamic variables: the pressure and the internal energy. The EPVS-FMDF is obtained by solving its modeled transport equation, in which the effect of convection appears in a closed form. The modeled EPVS-FMDF is employed for LES of a temporally developing mixing layer

PDF Simulations of Auto-Ignition in Internal Combustion Engines

Die Eigenschaften der Verbrennungsvorgänge in Verbrennungsmotoren bieten eine starke Motivation für die Annahme stochastischer Ansätze zur Modellierung dieser Prozesse. Eine neue Methodik wurde entwickelt zur Modellierung der Selbstzündung bei Verbrennungsmotoren. Diese Methodik basiert auf der Lösung der Transportgleichung für die Wahrscheinlichkeitsdichtefunktion für die Geschwindigkeit und Skalare

Large eddy simulation of dual-fuel combustion under ICE conditions

The present thesis aims at studying n-heptane/methanol dual-fuel combustion under internal combustion engine conditions and strives to improve the understanding of its ignition, combustion, and pollutant emission mechanisms. Large-eddy simulation (LES) coupled with Eulerian stochastic fields (ESF) approach is employed to simulate single/dual-fuel combustion in a constant-volume vessel to mimic the single/dual-fuel combustion in conventional/dual-fuel premixed engines. The experimental configuration from Engine Combustion Network (ECN) is considered as the baseline case in the simulations. The main works are summarized in two parts: model development and studies of the fundamental physics involved in dual-fuel combustion.First, the ESF approach with a novel modified method is proposed, implemented, and evaluated. Results show that the modified ESF method removes the numerical error in the element mass conservation and shows capability in predicting both premixed and non-premixed flames relevant to dual-fuel combustion. Second, LES of n-heptane single-fuel and n-heptane/methanol dual-fuel combustion is carried out and validated against ECN Spray-H experiments. A good agreement is obtained in terms of flow, combustion, and emissions characteristics. Finally, a parameter study is performed to investigate the effects of the dual-fuel strategies, including the primary fuel concentration, the ambient temperature, and the pilot fuel injection timing. It is concluded that: 1) The ambient methanol is found to have an effect of suppressing the two-stage ignition and heat release of n-heptane, this is more significant under high ambient methanol concentration conditions. 2) The effects of methanol on the n-heptane ignition and NOx formation are strongly dependent on the ambient temperatures. The retardation of the n-heptane high temperature ignition is more remarkable under low ambient temperatures. The NOx and soot in the dual-fuel case is lower than that of the single-fuel case in moderately high initial temperatures, while an opposite trend is observed in higher temperatures. 3) A late injection may lead to an overlap of the ambient methanol auto-ignition and the delivery of n-heptane. This overlap results in high soot and NOx formation

Three dimensional finite element modelling of non-Newtonian fluid flow through a wire mesh

Monofilament cloths are used as the separation media in filtration; woven wire cloths or screens are also used as the media in filters or to enhance the integrity of the filter medium in, for example, filter cartridges. A better understanding of the flow pattern in the woven structure is essential in examining the initial stages of cake filtration as well as the effect of weaves on fouling phenomena within a filter cloth. Due to the complex geometry of a woven cloth, three-dimensional modelling is necessary to correctly visualize the structure of the flow and hence to predict pressure losses. The modelling in a three-dimensional domain was handled using a finite element method which is known to cope with flow domains in complex geometries very effectively. The governing equations of continuity and momentum were solved by a mixed U-V-W-P finite element method and in conjunction with a first order Taylor-Galerkin scheme for temporal discretization. A secondary solution scheme based on a continuous Penalty finite element method in conjunction with theta time stepping method was also used to solve the governing equations. Two robust and reliable computer tools based on these sound and robust numerical techniques have been developed to simulate Newtonian and non-Newtonian fluid flow through a woven wire mesh. Purpose-designed test cases were used to validate the capability of the developed algorithms and were found to give expected numerical predictions. A selection of domains was used to investigate the effect of weave pattern, aperture to diameter ratio and Reynolds number on flow pattern and pressure drop. Based on these domains, simulations were successfully conducted to investigate fluid flow through four basic pore types in a plain weave, twill weave and satin weave. The flow fields in the interstices were illustrated using a commercial graphics software package. The results showed that the weave pattern has a profound effect on the fluid flow pattern and pressure drop across the wire mesh. Simulation results showed that plain weave gives the lowest pressure drop, while satin weave gives the highest pressure drop across the woven cloths. Fluid flow through a plain weave was further investigated in conjunction with the experimental studies of Rushton (1969) using water and Chhabra and Richardson (1985) using shear-thinning fluids. Simulations were tested against experimental data extracted from both studies. The close agreement of the results to those of the available experimental data in literature showed the accuracy and the reliability of the predictions. Personal communication with industrial experts and woven cloth manufacturers have confirmed industrial practice, whereby a plain weave is primarily used due to its lowest flow resistance. This showed that the developed model is capable of generating accurate results for flow of both Newtonian and non-Newtonian fluids through filter media. The model can be used by design engineers as a convenient and effective Computer Aided Design (CAD) tool for quantifying effects of pressure drop. The model can also be extended to describe particle capture on/in the wire mesh and woven filter cloths