High energy resummation of transverse momentum distributions:Higgs in gluon fusion

We derive a general resummation formula for transverse-momentum distributions of hard processes at the leading logarithmic level in the high-energy limit, to all orders in the strong coupling. Our result is based on a suitable generalization of high-energy factorization theorems, whereby all-order resummation is reduced to the determination of the Born-level process but with incoming off-shell gluons. We validate our formula by applying it to Higgs production in gluon fusion in the infinite top mass limit. We check our result up to next-to-leading order by comparison to the high energy limit of the exact expression and to next-to-next-to leading by comparison to NNLL order trasverse momentum (Sudakov) resummation, and we predict the high-energy behaviour at next$^3$-to-leading order. We also show that the structure of the result in the small transverse momentum limit agrees to all orders with general constraints from Sudakov resummation.Comment: 28 pages, 6 figures, Final version published in JHEP: several typos corrected (including in equations

Top Quark Pair Production beyond NNLO

We construct an approximate expression for the total cross section for the production of a heavy quark-antiquark pair in hadronic collisions at next-to-next-to-next-to-leading order (N$^3$LO) in $\alpha_s$. We use a technique which exploits the analyticity of the Mellin space cross section, and the information on its singularity structure coming from large N (soft gluon, Sudakov) and small N (high energy, BFKL) all order resummations, previously introduced and used in the case of Higgs production. We validate our method by comparing to available exact results up to NNLO. We find that N$^3$LO corrections increase the predicted top pair cross section at the LHC by about 4% over the NNLO.Comment: 34 pages, 9 figures; final version, to be published in JHEP; reference added, minor improvement

Combined threshold and transverse momentum resummation for inclusive observables

We present a combined resummation for the transverse momentum distribution of a colorless final state in perturbative QCD, expressed as a function of transverse momentum pT and the scaling variable x. Its expression satisfies three requirements: it reduces to standard transverse momentum resummation to any desired logarithmic order in the limit pT \ue2\u86\u92 0 for fixed x, up to power suppressed corrections in pT; it reduces to threshold resummation to any desired logarithmic order in the limit x \ue2\u86\u92 1 for fixed pT, up to power suppressed correction in 1 \ue2\u88\u92 x; upon integration over transverse momentum it reproduces the resummation of the total cross cross at any given logarithmic order in the threshold x \ue2\u86\u92 1 limit, up to power suppressed correction in 1 \ue2\u88\u92 x. Its main ingredient, and our main new result, is a modified form of transverse momentum resummation, which leads to threshold resummation upon integration over pT, and for which we provide a simple closed-form analytic expression in Fourier-Mellin (b, N) space. We give explicit coefficients up to NNLL order for the specific case of Higgs production in gluon fusion in the effective field theory limit. Our result allows for a systematic improvement of the transverse momentum distribution through threshold resummation which holds for all pT, and elucidates the relation between transverse momentum resummation and threshold resummation at the inclusive level, specifically by providing within perturbative QCD a simple derivation of the main consequence of the so-called collinear anomaly of SCET

Sviluppo e validazione di un modello di film fluido per simulazioni CFD di motori a combustione interna

A wall film model has been implemented in a customized version of KIVA code developed at University of Bologna. Under the hypothesis of `thin laminar ow' the model simulates the dynamics of a liquid wall film generated by impinging sprays. Particular care has been taken in numerical implementation of the model. The major phenomena taken into account in the present model are: wall film formation by impinging spray; body forces, such as gravity or acceleration of the wall; shear stress at the interface with the gas and no slip condition on the wall; momentum contribution and dynamic pressure generated by the tangential and normal component of the impinging drops; film evaporation by heat exchange with wall and surrounding gas. The model doesn't consider the effect of the wavy film motion and suppose that all the impinging droplets adhere to the film. The governing equations have been integrated in space by using a finite volume approach with a first order upwind differencing scheme and they have been integrated in time with a fully explicit method. The model is validated using two different test cases reproducing PFI gasoline and DI Diesel engine wall film conditions

Development of a chemical-kinetic database for the laminar flame speed under GDI and water injection engine conditions

Abstract The use of direct injection, supercharging, stoichiometric operation and reduction of the engine displacement, necessary to limit the specific consumption without reducing the power, makes the current spark ignition engines sensible to both the detonation and the increase of the inlet turbine temperature. The current research has therefore focused on the study of strategies aimed at reducing the risk of detonation using traditional and innovative solutions such as water injection. The application and optimization of these strategies can not ignore the knowledge of physical quantities characterizing the combustion such as the laminar flame speed. The laminar burning speed is an intrinsic property of the fuel and it is function of the mixture composition (mixture fraction and dilution) and of the thermodynamic conditions. The experimental measurements of the laminar flame speed available in the literature, besides not being representative of the pressure and temperature conditions characteristic of GDI engines, rarely report the effects of dilution by EGR or water vapor. To overcome the limitations of the experimental campaign it is possible to predict the value of the laminar flame speed resorting to numerical combustion models based on chemical kinetics. The increased performance of computing systems makes affordable the use of chemical schemes with a high number of species and reactions without facing an excessive temporal cost. In this work it is presented a methodology for the construction of a laminar flame speed database based on a non-reduced kinetic scheme and an open source solver (Cantera) for a commercial gasoline surrogate under the typical conditions of GDI engines with the addition of the effects of dilution with water and EGR

Evaluation of the effects of a Twin Spark ignition system on combustion stability of a high performance PFI engine

The continuous demand for high performances and low emissions engines leads the engine manufactures to set the operating range of combustion devices near to their stability limit. Combustion stability is closely related to the formation of the first ignition kernel: an effective way of lowering Cycle-by-Cycle Variation (CCV) is to enhance the start of combustion by means of multiple sparks. A Ducati engine was equipped with a Twin Spark ignition system and a consistent improvement in combustion stability arised for both part load and full load conditions. At part load a sensible reduction of cycle-by-cycle variability of indicated mean effective pressure was found, while at full load condition the twin spark configuration showed an increase of power, but with higher knocking tendency. The aim of this work is to better understand the root causes of the increased level of knock and to make a critical evaluation of most used knock indexes, by means of an accurate analysis of the experimental and simulated pressure signals. The numerical methodology based on a perturbation of the initial kernel by a statistical evaluation of mixture condition at ignition location. A lagrangian ignition model developed at University of Bologna was used, here modified to take into account the statistical distribution of mixture around the spark plugs. The RANS simulations proved to be accurate in representing all the main information related to combustion efficiency and knocking events. © 2015 The Authors. Published by Elsevier Ltd

basics on water injection process for gasoline engines

Abstract Actual and future limits to the global CO2 emissions and the necessity of a further reduction of the fossil non-renewable fuels have moved the automotive engine research toward new solutions. With focus on reciprocating internal combustion engines, the mass of CO2 emitted in the atmosphere is a function of the fuel consumption. Therefore, the designers are focusing their attention on both the drop of passive resistances and the improvement of the engine efficiency. As far as the latter is concerned, the reduction of in-cylinder temperature and the adoption of stoichiometric combustion on the full range of engine operation map are the most investigated solutions. Water injection is thought to help in fulfilling these goals thus contributing towards more efficient engines. The aim of the present work is to understand the basic thermophysical and chemical fundamentals governing the water injection application in modern downsized spark ignited engines. The investigation has been carried out with aid of CFD simulation by using AVL FIRE v.2017 solver

Development of a Emission Compliant, High Efficiency, Two-valve DI Diesel Engine for Off-road Application

Nowadays, environmental concerns are posing a great challenge to DI Diesel engines. Increasingly tightening emission limits require a higher attention on combustion efficiency. A high efficiency Diesel engine can be developed only mastering all the parameters that can affect the combustion and, therefore, NOx and soot emissions. In this scenario, computational fluid-dynamics can prove its power guaranteeing a deeper understanding of mixture formation process and combustion. In this work, the development of an engine in order to fulfill Tier 4i emission standard will be presented, the Tier 4i compliance must be reached without an excessive increase of the final cost of the engine. Originally, the engine was a two-valve engine supplied with a DPF, since no SCR aftertreatment is supplied, NOx emission target are achieved through external exhaust gas recirculation and retarding the start of injection. Through combustion process simulations, performed with the CFD code KIVA3D, varying different geometric parameters and the intensity of the swirl ratio, the interaction between the swirl flow field, generated by the intake duct, the reverse squish motion, and motions aerodynamically generated by spray has been investigated leading to a better interaction between the flow field, the fuel spray and the piston bowl geometry and to the definition of a new engine lay-out. The study shows how, given the need of retarded injection for limiting NOx emission, the decrease of swirl ratio, when combined with a proper piston bowl design, allows a significant decrease of soot emissions and the achievement of Tier 4i emission standard. The study has been validated comparing the intake phase simulations, performed with the CFD code Fire v2009 v3, followed by the combustion process performed with the KIVA3D code, with the experimental result obtained from the engine assembled following the developed design. © 2013 The Authors