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

Statistically consistent term structures have affine geometry

This paper is concerned with finite dimensional models for the entire term structure for energy futures. As soon as a finite dimensional set of possible yield curves is chosen, one likes to estimate the dynamic behaviour of the yield curve evolution from data. The estimated model should be free of arbitrage which is known to result in some drift condition. If the yield curve evolution is modelled by a diffusion, then this leaves the diffusion coefficient open for estimation. From a practical perspective, this requires that the chosen set of possible yield curves is compatible with any obtained diffusion coefficient. In this paper, we show that this compatibility enforces an affine geometry of the set of possible yield curves.Comment: 17 page

Explicit Local density bounds for It\^o-processes with irregular drift

We find explicit upper bounds for the density of marginals of continuous diffusions where we assume that the diffusion coefficient is constant and the drift is solely assumed to be progressively measurable and locally bounded. In one dimension we extend our result to the case that the diffusion coefficient is a locally Lipschitz-continuous function of the state. Our approach is based on a comparison to a suitable doubly reflected Brownian motion whose density is known in a series representation.Comment: 13 page

A sharp upper bound for the expected occupation density of It\^o processes with bounded irregular drift and diffusion coefficients

We find explicit and optimal upper bounds for the expected occupation density for an It\^o-process when its drift and diffusion coefficients are unknown under boundedness and ellipticity conditions on the coefficients. This is related to the optimal bound for the expected interval occupation found in Ankirchner and Wendt(2021). In contrast, our bound is for a single point and the resulting formula is less involved. Our findings allow us to find explicit upper bounds for mean path integrals.Comment: 20 page