| 1. |
- Pollack, Martin, et al.
(författare)
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Zero-flux approximations for multivariate quadrature-based moment methods
- 2019
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 1090-2716 .- 0021-9991. ; 398
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 2. |
- Pütz, Michele, 1988
(författare)
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Numerical Modeling of Atomization in Spray Systems
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Dispersed multiphase flows refer to dynamic systems comprising two or more phases where at least one phase is in the form of fine particles evolving in and interacting with a surrounding fluid. Spray systems fall into that category. Several technical applications highlight the significance of sprays, one of which is the injection of liquid fuel in propulsion systems, where the spray formation, vaporization and subsequent mixing prior to combusion determine fuel efficiency and the emission of pollutants that are hazardous to human health and nature. Optimization of such systems requires the understanding of spray physics. While theoretical analysis and experiments remain essential methods with regard to the optimization of such systems, the advance in computer performance over the past few decades has made numerical simulation an additional powerful tool to improve spray systems. However, the existence of physical and predictive models is crucial. This thesis is concerned with the physical phenomena that are present in spray systems and the transfer to suitable computational models. In terms of spray physics, the focus is on atomization which refers to the disintegration of liquid structures. Another central aspect of spray modeling is the representation of the particulate phase. The numerical models studied as part of this work are the one-dimensional turbulence model for the breakup of a liquid jet combined with standard Lagrangian methods as well as a family of Eulerian population balance models, the so-called quadrature-based moment methods. Numerical investigations were carried out on a gasoline spray as well as less complex configurations and give many suggestions for future research.
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| 3. |
- Pütz, Michele, 1988, et al.
(författare)
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Numerical simulation of a gasoline spray using one-dimensional turbulence for primary atomization
- 2020
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Ingår i: ICLASS 2018 - 14th International Conference on Liquid Atomization and Spray Systems.
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Konferensbidrag (refereegranskat)abstract
- Predictive and reliable simulations have the potential to constitute a valuable tool for the optimization of spray systems if accurate submodels are developed for the entire range of the governing processes. The primary breakup of the turbulent liquid jet is one the most important mechanisms in sprays, yet the least developed in terms of numerical modeling. The most accurate method to simulate primary breakup is the proper resolution of liquid-gas interfaces and turbulent flow structures. However, a wide range of relevant length and time scales implicate grid requirements that are often prohibitive for real engineering applications. The most widely used method in practice is still the representation of both the continuous liquid core and the dispersed phase by means of discrete Lagrangian particles evolving in and interacting with the Eulerian gas phase. The available models for primary breakup are mainly phenomenological and involve a number of empirical constants. The one-dimensional turbulence (ODT) model is an alternative stochastic approach to model turbulence in flows with a dominant direction of property gradients. The stochastic representation of turbulent eddies on a one-dimensional domain enables high resolution at moderate computational costs. Applications of ODT to atomization revealed a great potential in recent studies. The objective of the present study is to combine ODT as a primary breakup model with a conventional Eulerian-Lagrangian method for the further spray evolution in order to asses ODT as a submodel in full spray models. Our numerical investigations were conducted on the ECN spray G, a gasoline-like, evaporating spray. The results in terms of spray penetration are encouraging, though the applicability of ODT to the transient injection phase and effects on additional spray characteristics require further investigation.
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