Numerical modelling of compressible turbulent premixed hydrogen flames

Turbulent combustion has a profound effect on the way we live our lives; homes and businesses predominantly rely on power generated by burning some form of fuel, and the vast majority of transport of passengers and cargo are driven by combustion. Fossil fuels remain readily available and relatively cheap, and so will continue to power the modern world for the foreseeable future. Combustion of fossil fuels produces emissions that detrimentally affect air quality, particularly in highly-populated cities, and are also widely believed to be contributing to global climate change. Consequently, increasing attention is being focused on alternative fuels, increased efficiency and reduced emissions. One alternative fuel is hydrogen, which introduces challenges in end-usage, storage and safety that are not encountered with more conventional fuels. Advances in computational power and software technology means that numerical simulation has a growing role in the development of combustors and safety evaluation. Despite these advances, many challenges remain; the broad range of time and length scales involved are coupled with complex thermodynamics and chemistry on top of turbulent fluid mechanics, which means that detailed simulations of even relatively-simple burners are still prohibitively expensive. Engineering turbulent flame models are required to reduce computational expense, and the challenge is to retain as much of the flow physics as possible. Furthermore, the choice of numerical approach has a significant effect on the quality of simulation, and different target applications place different demands on the numerical scheme. In the case of hydrogen explosion, the approach needs to be able to capture a range of physical behaviours including turbulence, low-speed deflagration, high-speed shock waves and potentially detonations. One such numerical approach that has enjoyed widespread success is finite volumes schemes based on the Godunov method. These methods perform well at all speeds, and have positive shock-capturing capability, but recent studies have demonstrated difficulties with numerical stability for more complex thermodynamics, specifically in the case of fully-conservative methods for multi-component fluids with varying thermodynamic properties. A recent development is the so-called double-flux method, which retains many of the positive properties of the fully-conservative approaches and does not suffer from the same numerical instabilities, but is quasi-conservative and involves additional computational expense. The present work consolidates the state-of-the-art in the literature, and considers two equation sets, based on mass fraction and volume fraction, respectively, along with fully-conservative and quasiconservative schemes. Comprehensive validation and evaluation of the different approaches is presented. It was found that both quasi-conservative approaches performed well, with a better conservative behaviour for the quasi-conservative volume fraction, but a better stability for the quasi-conservative mass fraction. Finally, the numerical tool developed is applied to turbulent combustion of premixed hydrogen in the context of the semi-confined experiments from the University of Sydney. The LES results showed an good overall agreement with the experimental data, and the critical parameters such as overpressure and flame speed where globally well captured, highlighting the large potential of LES for safety analysis

Exoplanet Clouds

Clouds also form in atmospheres of planets that orbit other stars than our Sun, in so-called extrasolar planets or exoplanets. Exoplanet atmospheres can be chemically extremely rich. Exoplanet clouds are therefor made of a mix of materials that changes throughout the atmosphere. They affect the atmospheres through element depletion and through absorption and scattering, hence, they have a profound impact on the atmosphere's energy budget. While astronomical observations point us to the presence of extrasolar clouds and make first suggestions on particle sizes and material compositions, we require fundamental and complex modelling work to merge the individual observations into a coherent picture. Part of this is to develop an understanding for cloud formation in non-terrestrial environments.Comment: Review paper for Annual Review of Earth and Planetary Sciences (26 pages), accepted for publicatio

Coupled constitutive relations: a second law based higher order closure for hydrodynamics

In the classical framework, the Navier-Stokes-Fourier equations are obtained through the linear uncoupled thermodynamic force-flux relations which guarantee the non-negativity of the entropy production. However, the conventional thermodynamic description is only valid when the Knudsen number is sufficiently small. Here, it is shown that the range of validity of the Navier-Stokes-Fourier equations can be extended by incorporating the nonlinear coupling among the thermodynamic forces and fluxes. The resulting system of conservation laws closed with the coupled constitutive relations is able to describe many interesting rarefaction effects, such as Knudsen paradox, transpiration flows, thermal stress, heat flux without temperature gradients, etc., which can not be predicted by the classical Navier-Stokes-Fourier equations. For this system of equations, a set of phenomenological boundary conditions, which respect the second law of thermodynamics, is also derived. Some of the benchmark problems in fluid mechanics are studied to show the applicability of the derived equations and boundary conditions.Comment: 20 pages, 6 figures, Proceedings of the Royal Society A (Open access article

Computational fluctuating fluid dynamics

This paper describes the extension of a recently developed numerical solver for the Landau-Lifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for the stochastic fluxes and in mixtures due to couplings of energy and concentration fluxes (e.g., Soret effect). We present various numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate good agreement with theoretical results and molecular simulatio

Modelling In-situ Upgrading (ISU) of heavy oil using dimensionless analysis and operator splitting method

The In-Situ Upgrading (ISU) of bitumen and oil shale is a very challenging process to model numerically because a large number of components need to be modelled using a system of equations that are both highly non-linear and strongly coupled. In addition to the transport of heat by conduction and convection, and the change of properties with varying pressure and temperature, these processes involve transport of mass by convection, evaporation, condensation and pyrolysis chemical reactions. The behaviours of these systems are difficult to predict as relatively small changes in the material composition can significantly change the thermophysical properties. Accurate prediction is further complicated by the fact that many of the inputs needed to describe these processes are uncertain, e.g. the reaction constants and the temperature dependence of the material properties. The large number of components and chemical reactions involves a non-linear system that is often too large for full field simulation using the Fully Implicit Method (FIM). Operator splitting (OS) methods are one way of potentially improving computational performance. Each numerical operator in a process is modelled separately, allowing the best solution method to be used for the given numerical operator. A significant drawback to the approach is that decoupling the governing equations introduces an additional source of numerical error, known as splitting error. Obviously the best splitting method for modelling a given process is the one that minimises the splitting error whilst improving computational performance over that obtained from using a fully implicit approach. Although operator splitting has been widely used for the modelling of reactive-transport problems, it has not yet been applied to models that involve the coupling of mass transport, heat transfer and chemical reactions. One reason is that it is not clear which operator splitting technique to use. Numerous such techniques are described in the literature and each leads to a different splitting error, which depends significantly on the relative importance of the mechanisms involved in the system. While this error has been extensively analysed for linear operators for a wide range of methods, the results observed cannot be extended to general non-linear systems. It is therefore not clear which of these techniques is most appropriate for the modelling of ISU. Analysis using dimensionless numbers can provide a useful insight into the relative importance of different parameters and processes. Scaling reduces the number of parameters in the problem statement and quantifies the relative importance of the various dimensional parameters such as permeability, thermal conduction and reaction constants. Combined with Design of Experiments (DOE), which allows quantification of the impact of the parameters with a minimal number of numerical experiments, dimensionless analysis enables experimental programmes to be focused on acquiring the relevant data with the appropriate accuracy by ranking the different parameters controlling the process. It can also help us design a better splitting method by identifying the couplings that need to be conserved and the ones that can be relaxed. This work has three main objectives: (1) to quantify the main interactions between the heat conduction, the heat and mass convection and the chemical reactions, (2) to identify the primary parameters for the efficiency of the process and (3) to design a numerical method that reduces the CPU time of the simulations with limited loss in accuracy. We first consider a simplified model of the ISU process in which a solid reactant decomposes into non-reactive gas. This model allows us to draw a parallel between the in-situ conversion of kerogen and the thermal decomposition of polymer composite when used as heat-shield. The model is later extended to include a liquid phase and several reactions. We demonstrate that a ISU model with nf fluid components, ns solid components and k chemical reactions depends on 9+k*(3+nf+ns-2)+8nf+2ns dimensionless numbers. The sensitivity analysis shows that (1) the heat conduction is the primary operator controlling the time scale of the process and (2) the chemical reactions control the efficiency of the process through the extended Damköhler numbers, which quantify the ratio of chemical rate to heat conduction rate at the heater temperature for each reaction in the model. In the absence of heat loss and gravity effects, we show that the ISU process is most efficient at a heater temperature for which the minimum of the extended Damköhler numbers of all reactions included in the model was between 10 and 20. For the numerical method, the standard Iterative Split Operator (ISO) does not perform well due to many convergence failures, whereas the standard Sequential Split Operator (SSO) and the Strang-Marchuk Split Operator (SMSO) give large discretization errors. We develop a new method, called SSO-CKA, which has smaller discretization error. This method simply applies SSO with three decoupled operators: the heat conduction (operator $C$), the chemical reactions (operator $K$) and the heat and mass convection (operator $A$), applied in this order. When we apply SSO-CKA with the second-order trapezoidal rule (TR) for solving the chemical reaction operator, we obtain a method which generally gives smaller discretization errors than FIM. We design an algorithm, called SSO-CKA-TR-AIM, which is faster and generally more accurate than FIM for simulations with a kinetic model including a large number of components that could be regrouped into a small number of chemical classes for the advection and heat conduction operator. SSO-CKA works best for ISU models with small reaction enthalpies and no other reaction than pyrolysis reactions, but can give a large discretization method for ISU models with non-equilibrium reactions.Open Acces