Martin Pollack’s research while affiliated with Technische Universität Darmstadt and other places

The ignition of non-premixed n-dodecane-air flames is studied in a highly transient counterflow configuration under diesel engine operating conditions. The one-dimensional transient counterflow is configured such that ignition is initially physically inhibited through high strain rates. In a short relaxation period the inflow velocities (thereby the strain rate) are lowered and ignition can occur, a behaviour similarly observed in spray flames. The non-premixed flame, which is igniting in this unsteady flow environment, is computed with direct chemistry and tabulated chemistry based on the unsteady flamelet progress variable approach (UFPV). The flamelet look-up table is constructed from igniting unsteady flamelets considering also the parameter range between stable and unstable branches of the characteristic S-shaped curve which is obtained via a continuation method. The mixture fraction, the progress variable, and the local stoichiometric scalar dissipation rate serve as control variables for the three-dimensional table. Particular attention is put on the inclusion of thermal expansion effects and the treatment of the progress variable source term to capture the onset of ignition. Besides varying strain effects, the igniting flame exhibits low temperature chemistry and multi-stage ignition behaviour which is particular challenging for the UFPV modeling. By direct comparison to the reference solution the predictive capabilities of the UFPV approach are analyzed and assessed in detail. Furthermore, the influence of table resolution on computational efficiency is discussed. The systematic analysis and validation of the UFPV approach in the transient counterflow configuration fills a specific gap in the literature and underlines the fidelity of the approach for flames subject to complex transient processes. Furthermore, the 1D configuration may serve as an environment for adjusting and optimizing UFPV tabulation strategies prior to their application to more complex 3D CFD simulations such as spray LES.

Many particulate systems occurring in nature and technology are adequately described by a number density function (NDF). The numerical solution of the corresponding population balance equation (PBE) is typically accompanied by high computational costs. Quadrature-based moment methods are an approach to reduce the computational complexity by solving only for a set of moments associated with the NDF employing Gaussian quadrature rules to close the moment equations derived from the PBE. The evolution of a population of inertial particles dispersed in a turbulent fluid is governed by a PBE with a phase-space diffusion term as a result of random microscale fluctuations. Considerations on the microscopic behavior concerning the momentum exchange between fluid and dispersed particles suggest that this diffusion term is nonlinear and nonsmooth. The resulting integral terms in the derived moment equations entail large approximation errors when using Gaussian quadrature rules for closure. In this work, we propose a modification of the quadrature method of moments (QMOM), namely the Gauss/anti-Gauss-QMOM (GaG-QMOM), making use of anti-Gaussian quadrature formulae to reduce the large errors due to this particular form of diffusion. This new method is investigated in a series of simple one-dimensional test cases with analytical reference solutions. Moreover, we propose a realizability-preserving variation of the strong-stability preserving Runge-Kutta (RKSSP) schemes that is suited to problems involving phase-space diffusion. Besides the observation that the modified second-order RKSSP scheme can serve as a realizability-preserving alternative to the standard RKSSP scheme of the same order, the numerical results reveal that, compared to the standard QMOM, the GaG-QMOM can reduce the large errors by one to two orders of magnitude.

This article reports on a novel design of an AdBlue mixing unit to reduce urea deposits at low temperatures in diesel exhaust. The main principle of the mixer includes the injection of AdBlue in an axisymmetric swirling flow, which is achieved by splitting the exhaust stream and off‐centred introduction of the sub‐flows. Crucial geometric parameters were analysed by CFD simulations towards pressure loss, flow field and spray morphology. Deposit formation was experimentally investigated on three upscaling levels implying an optical test bench, a diesel engine test bench and a hydraulic excavator. In particular, the studies with the hydraulic excavator showed neither deposits nor critical back pressure. Overall, the experiments substantiated the working principle of the AdBlue mixer.

Transported probability density function (PDF) methods are widely used to model turbulent flames characterized by strong turbulence-chemistry interactions. Numerical methods directly resolving the PDF are commonly used, such as the Lagrangian particle or the stochastic fields (SF) approach. However, especially for premixed combustion configurations, characterized by high reaction rates and thin reaction zones, a fine PDF resolution is required, both in physical and in composition space, leading to high numerical costs. An alternative approach to solve a PDF is the method of moments, which has shown to be numerically efficient in a wide range of applications. In this work, two Quadrature-based Moment closures are evaluated in the context of turbulent premixed combustion. The Quadrature-based Moment Methods (QMOM) and the recently developed Extended QMOM (EQMOM) are used in combination with a tabulated chemistry approach to approximate the composition PDF. Both closures are first applied to an established benchmark case for PDF methods, a plug-flow reactor with imperfect mixing, and compared to reference results obtained from Lagrangian particle and SF approaches. Second, a set of turbulent premixed methane-air flames are simulated, varying the Karlovitz number and the turbulent length scale. The turbulent flame speeds obtained are compared with SF reference solutions. Further, spatial resolution requirements for simulating these premixed flames using QMOM are investigated and compared with the requirements of SF. The results demonstrate that both QMOM and EQMOM approaches are well suited to reproduce the turbulent flame properties. Additionally, it is shown that moment methods require lower spatial resolution compared to SF method.

Spray modeling requires a proper representation of the dispersed phase and involves models for a variety of physical phenomena. On the population scale, a properly formulated population balance equation provides a complete statistical description of the particle system. However, in most cases the high dimensionality entails prohibitive computational costs. Quadrature‐based moment methods (QBMM) limit the description of particle populations to a set of only a few moments and thus considerably reduce computational complexity. In order to apply QBMM to sprays, models for many involved physical processes must be formulated consistently in the QBMM‐context. We study secondary droplet breakup with QBMM using a simple well‐established spray breakup model and simplified setups.

Transported probability density function (PDF) methods are widely used to model turbulent flames characterized by strong turbulence-chemistry interactions. Numerical methods directly resolving the PDF are commonly used, such as the Lagrangian particle or the stochastic fields (SF) approach. However, especially for premixed combustion configurations, characterized by high reaction rates and thin reaction zones, a fine PDF resolution is required, both in physical and in composition space, leading to high numerical costs. An alternative approach to solve a PDF is the method of moments, which has shown to be numerically efficient in a wide range of applications. In this work, two Quadrature-based Moment closures are evaluated in the context of turbulent premixed combustion. The Quadrature-based Moment Methods (QMOM) and the recently developed Extended QMOM (EQMOM) are used in combination with a tabulated chemistry approach to approximate the composition PDF. Both closures are first applied to an established benchmark case for PDF methods, a plug-flow reactor with imperfect mixing, and compared to reference results obtained from Lagrangian particle and SF approaches. Second, a set of turbulent premixed methane-air flames are simulated, varying the Karlovitz number and the turbulent length scale. The turbulent flame speeds obtained are compared with SF reference solutions. Further, spatial resolution requirements for simulating these premixed flames using QMOM are investigated and compared with the requirements of SF. The results demonstrate that both QMOM and EQMOM approaches are well suited to reproduce the turbulent flame properties. Additionally, it is shown that moment methods require lower spatial resolution compared to SF method.

The evolution of polydisperse systems is governed by population balance equations. A group of efficient solution approaches are the moment methods, which do not solve for the number density function (NDF) directly but rather for a set of its moments. While this is computationally efficient, a specific challenge arises when describing the fluxes across a boundary in phase space for the disappearance of elements, the so-called zero-flux. The main difficulty is the missing NDF-information at the boundary, which most moment methods cannot provide. Relevant physical examples are evaporating droplets, soot oxidation or particle dissolution. In general, this issue can be solved by reconstructing the NDF close to the boundary. However, this was previously only achieved with univariate approaches, i.e. considering only a single internal variable. Many physical problems are insufficiently described by univariate population balance equations, e.g. droplets in sprays often require the temperature or the velocity to be internal coordinates in addition to the size. In this paper, we propose an algorithm, which provides an efficient multivariate approach to calculate the zero-fluxes. The algorithm employs the Extended Quadrature Method of Moments (EQMOM) with Beta and Gamma kernel density functions for the marginal NDF reconstruction and a polynomial or spline for the other conditional dimensions. This combination allows to reconstruct the entire multivariate NDF and based on this, expressions for the disappearance flux are derived. An algorithm is proposed for the whole moment inversion and reconstruction process. It is validated against a suite of test cases with increasing complexity. The influence of the number of kernel density functions and the configuration of the polynomials and splines on the accuracy is discussed. Finally, the associated computational costs are evaluated.

Recently improved knowledge about key processes for the formation and growth of soot particles lead to very extensive soot models describing several kinetic pathways for particle nucleation and growth in detail. One of these models has been proposed by D'Anna and coworkers (D'Anna et al., 2010, Sirignano et al., 2010). In these original studies, the multivariate formulation was solved with a sectional approach, while a more recent study (Salenbauch et al., 2017) also showed the suitability of moment methods such as the Conditional Quadrature Method of Moments (CQMOM) (Yuan et al., 2011). However, being a moment method, CQMOM does not allow to directly access the soot particle size distribution (PSD). This prevents the consistent comparability of CQMOM results to soot measurements based on a scanning mobility particle sizer (SMPS). Furthermore, the comparison to laser-induced fluorescence (LIF) experiments is also limited, as the LIF signal only represents small particles and their concentration is only extractable from the simulation results if the PSD shape is known. The aim of this study is to extend the previously developed CQMOM soot model by a PSD reconstruction step applying the concept of entropy maximization. Maintaining the efficiency of the CQMOM moment inversion algorithm to close the moment equations, the model extension enables to evaluate the diameter-based PSD in a post-processing step without prescribing a specific shape as input. The updated algorithm is applied to simulate soot formation in two different burner-stabilized premixed C2H4/O2/N2 flames with a very lightly sooting (C/O = 0.67) and a heavily sooting (C/O = 0.77) character. Numerical results are compared to recently published LIF, laser-induced incandescence (LII) and SMPS measurement data. The analysis investigates the model's capability to predict phenomena such as uni- or bimodal distribution shapes and the transition of small nanostructures to agglomerates in the two target flames both of which exhibit very different sooting behaviour.

In this work, a detailed kinetic mechanism for soot formation and evolution (D'Anna et al. 2010) is implemented in a method of moments framework using the concept of ‘Conditional Quadrature Method of Moments’ (CQMOM) (Yuan and Fox, 2011). Particle nucleation and growth pathways are described in detail tracking moments of the number density function (NDF) for large PAHs, soot clusters and agglomerates in both stable and radical forms. Individual entities of these groups are characterized by both their size and their H/C ratio, the latter providing information on the chemical structure and the reactivity of the particles. This leads to a multivariate population balance statement. The CQMOM implementation of the soot model is then applied to predict particle formation in a lightly sooting burner-stabilized premixed ethylene flame with an equivalence ratio of ϕ = 2.1. Several experimental data sets for this target flame are available in the literature and they are used in this study for comparison with the simulation results. The suitability of the soot model to predict particle matter under such conditions is shown, as both the onset of soot formation by nucleation and the subsequent growth are captured. Modeling results offer further insights into the relevance of agglomeration and dehydrogenation in this lightly sooting flame.