Right Engel elements of stability groups of general series in vector spaces

Let V be an arbitrary vector space over some division ring D, L a general series of subspaces of V covering all of V \ {0} and S the full stability subgroup of L in GL(V). We prove that always the set of bounded right Engel elements of S is equal to the w-th term of the upper central series of S and that the set of right Engel elements of S is frequently equal to the hypercentre of S

On the fixed-point set of an automorphism of a group

Let Ø be an automorphism of a group G. Under variousfiniteness or solubility hypotheses, for example under polycyclicity, the commutator subgroup [G; Ø] has finite index in G if thefixed-point set CG(Ø) of Ø in G isfinite, but not conversely, even for polycyclic groups G. Here we consider a stronger, yet natural, notion of what it means for [G;Ø] to have finite index' in G and show that in many situations, including G polycyclic, it is equivalent to CG(Ø) being finite

Automorphism groups of polycyclic-by-finite groups and arithmetic groups

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences of K(\Gamma, 1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory

On groups of finite Prüfer rank

Let G be a group of finite rank and π any finite set of primes. We prove that G contains a characteristic subgroup H of finite index such that every finite π-image of H is nilpotent. Our conclusions are stronger if G is also soluble

On groups of finite rank

We study the structure of groups of finite (Prufer) rank in a very wide class of groups and also of central extensions of such groups. As a result we are able to improve, often substantially, on a number of known numerical bounds, in particular on bounds for the rank (resp. Hirsch number) of the derived subgroup of a group in terms of the rank (resp. Hirsch number) of its central quotient and on bounds for the rank of a group in terms of its Hirsch numbe

Ignition and flame stabilisation of primary reference fuel sprays at engine-relevant conditions

This study aims to investigate the underlying processes governing ignition and flame stabilisation in compression-ignition (CI) engine-relevant conditions. The experiments feature a canonical configuration with a single fuel jet injected into a constant-volume combustion chamber. Primary reference fuels (PRFs), including PRF100 (neat iso-octane, a gasoline surrogate), PRF80 (a blend of 80 vol.% iso-octane and 20 vol.% n-heptane) and PRF0 (neat n-heptane, a diesel surrogate), were tested to simulate changes in fuel ignition quality inside a quiescent steady environment with an ambient density of 22.8 kg/m3 and an O2 concentration of 15 vol.%. The ambient gas temperatures were controlled at 1150 K (PRF100), 1120 K (PRF80) and 900 K (PRF0), in order to adapt to the fuel reactivity so that a constant ignition delay of 1.15 ms can be achieved for all blends. This approach was employed in order to substantially reduce the effect of fuel-oxidiser mixing prior to ignition while highlighting the effect of fuel chemistry on the ignition process and flame evolution. Under the test conditions of this study, optical imaging reveals that the blends with higher iso-octane content exhibit a faster spreading of combustion after ignition and establish a steady lifted flame that is closer to the nozzle. Imaging by CH2O-PLIF indicates that blends with higher iso-octane content produce CH2O that is distributed across larger portions of the jet at an earlier timing when compared to neat n-heptane that shows a propagating first-stage ignition through the fuel jet. Supporting unsteady flamelet calculations are presented to investigate the effect of chemistry and turbulent mixing. The flamelet calculations agree qualitatively in several respects to the experiments, especially in the spatial and temporal trends for CH2O production and consumption. Synthesis of the flamelet and experimental results suggests that for the iso-octane-containing fuels, CH2O is formed via single-stage ignition reactions rather than exhibiting the typical two-stage ignition behaviour which is found in the pure n-heptane fuel case. Furthermore, the flamelet calculations suggest high-temperature ignition occurs first in lean mixtures in the iso-octane-containing fuel cases, but in rich mixtures for the PRF0 case. If autoignition is the mode of flame stabilisation, this provides an explanation for why the PRF100 and PRF80 cases stabilise further upstream, since lean mixtures have longer residence times, experience lower scalar dissipation rate, and may be more likely to be exposed to a supporting peripheral reservoir of hot products, should one exist. Overall, this study provides insights into the roles of fuel chemistry and turbulent mixing on the ignition and combustion behaviour of PRFs under engine-relevant conditions

Mechanisms of NO<inf>x</inf>Production and Heat Loss in a Dual-Fuel Hydrogen Compression Ignition Engine

The combustion process of a homogeneous hydrogen charge in a small-bore compression ignition engine with diesel-pilot ignition was simulated using the CONVERGE computational fluid dynamics code. Analysis of the simulation results aimed to understand the processes leading to NOx production and heat loss in this combustion strategy, and their dependence on the hydrogen fuel energy fraction. Previous experimental results demonstrated promising performance, but this comes with a penalty in increased NOx emissions and potentially higher heat losses. The present study aims to enhance understanding of the mechanisms governing these phenomena. The simulated engine was initialised with a lean homogeneous hydrogen-air mixture at BDC and n-dodecane was injected as a diesel surrogate fuel near TDC. The simulations were validated based on experimental results for up to 50% hydrogen energy fraction, followed by an exploratory study with variation of the energy fraction from 0% to 90%. The addition of hydrogen increased the ignition delay and changed the combustion mode from typical diesel combustion to a premixed burn involving flame propagation. The causes of NOx emissions and heat loss trends in the simulations are investigated through an analysis of the temperature and equivalence ratio distributions in the engine. The results show that NOx production peaks at approximately 50% hydrogen, before decreasing as combustion becomes more premixed, which is shown to result in lower peak temperature. Heat loss is significant at all hydrogen energy fractions, but highest at intermediate values. Differences in the wall heat transfer are driven by the near-wall equivalence ratio, turbulence, and combustion phasing

A Numerical Investigation of Mixture Formation and Combustion Characteristics of a Hydrogen-Diesel Dual Direct Injection Engine

A hydrogen-diesel dual direct injection (H2DDI) combustion strategy in a compression-ignition engine is investigated numerically, reproducing the configuration of previous experimental investigations. These experiments demonstrated the potential of up to 50% diesel substitution by hydrogen while maintaining high engine efficiency; nevertheless, the emission of NOx increased compared with diesel operation and was strongly dependent on the hydrogen injection timing. This implies the efficiency and NOx emission are closely associated with hydrogen charge stratification; however, the underlying mechanisms are not fully understood. Aiming to highlight the hydrogen injection-timing influence on hydrogen/air mixture stratification and engine performance, the present study numerically investigates the mixture formation and combustion process in the H2DDI engine concept using Converge, a three-dimensional fluid dynamics simulation code. Increased hydrogen stratification levels are realised by retarding the hydrogen injection timing from 180 °CA to 40 °CA bTDC at fixed energy substitution ratio of 50%, as in the experiments. The simulations are validated against the measured pressure and apparent heat release rate traces. The simulation results show that early hydrogen injection yields an almost homogeneous mixture with entire hydrogen charge being in fuel-lean conditions, leading to a primarily premixed combustion process of the hydrogen fuel. The intermediate injection timings produce a moderately stratified hydrogen mixture with much of the hydrogen at near-stoichiometric conditions, which achieves the highest engine efficiency but also the highest NOx emissions. The late injection forms a highly stratified charge with most hydrogen mixtures in fuel-rich conditions, presenting a mixing-controlled combustion process. This combustion mode induces the lowest wall heat loss and the lowest NOx emissions, but yields a relatively high fraction of unburnt hydrogen and efficiency penalty

Hydrogen-diesel dual-fuel direct-injection (H2DDI) combustion under compression-ignition engine conditions

This study investigates the ignition and combustion characteristics of interacting diesel-pilot and hydrogen (H2) jets under simulated compression-ignition engine conditions. Two converging single-hole injectors were used to inject H2 and diesel-pilot jets into an optically accessible constant-volume combustion chamber (CVCC). The parameters varied include fuel injection sequence, timing between injections, and ambient temperature (780–890 K). The results indicate that when diesel-pilot is injected before H2, with increasing time separation, the burnt diesel products mix and cool down, requiring longer jet-jet interaction to ignite the H2 jet. When H2 is injected before diesel-pilot, the H2-air mixing amount prior to pilot-fuel igniting impacts the combustion spreading through the H2 jet. If ignition of the H2 jet occurs beyond its end-of-injection (EOI), the H2 mixture zone where the pilot-diesel interacts with becomes too lean for combustion. At lower ambient temperatures, the combustion variability increases, attributed to the diesel-pilot lean out

An evaluation of gas-phase micro-mixing models with differential mixing timescales in transported PDF simulations of sooting flame DNS

The use of transported probability density function (TPDF) models to predict soot has the strong advantage that the effects of turbulent fluctuations on soot source terms can be rigorously accounted for. However, soot processes are closely coupled to gas-phase composition. Among the open issues for gas-phase micro-mixing is the species-dependence of mixing timescales. The objective is to carry out an evaluation on the effect of incorporating differential mixing timescales among gas-phase species in a TPDF simulation for soot prediction. A DNS having the configuration of a temporally evolving, non-premixed ethylene flame with a four-step, three-moment soot model is considered as the target for evaluation. The DNS dataset is applied to provide key inputs for TPDF simulations to limit the sources of error to micro-mixing. TPDF simulations with the interaction by exchange with the mean (IEM) and modified Curl (MC) models, which impose the same mixing timescale to all species, underpredict soot mass fraction and overpredict extinction levels regardless of the prescribed mixing frequency. By incorporating differential mixing timescales among gas-phase species, IEM-DD and MC-DD models yield notable improvement in predictions of the overall extinction and soot levels, highlighting the benefit of accounting for differential mixing timescales. A TPDF simulation with the Euclidean minimum spanning tree (EMST) model yields even better predictions, illustrating that the localness in composition space remains a critical issue. The indicated species mixing frequencies by the EMST model are shown to follow the DNS results qualitatively, illustrating that the micro-mixing process based on the Euclidean distance in composition space reproduces to a certain extent the differential mixing timescales due to reaction. Finally, it is shown that incorporating differential mixing timescales of soot moments is expected to have limited value as the mixing timescales of soot moments are sufficiently large to safely neglect soot mixing