Modelling of automotive fuel droplets heating and evaporation - mathematical tools and approximations

New mathematical tools and approximations developed for the analysis of automotive fuel droplet heating and evaporation are summarised. The approach to modelling biodiesel fuel droplets is based on the application of the Discrete Component Model (DCM), while the approach to modelling Diesel fuel droplets is based on the application of the recently developed multi-dimensional quasi-discrete model. In both cases, the models are applied in combination with the Eective Thermal Conductivity/Eective Diusivity model and the implementation in the numerical code of the analytical solutions to heat transfer and species diusion equations inside droplets. It is shown that the approximation of biodiesel fuel by a single component leads to under-prediction of droplet evaporation time by up to 13% which can be acceptable as a crude approximation in some applications. The composition of Diesel fuel was simpli ed and reduced to only 98 components. The approximation of 98 components of Diesel fuel with 15 quasi-components/components leads to under-prediction of droplet evaporation time by about 3% which is acceptable in most engineering applications. At the same time, the approximation of Diesel fuel by a single component and 20 alkane components leads to a decrease in the evaporation time by about 19%, compared with the case of approximation of Diesel fuel with 98 components. The approximation of Diesel fuel with a single alkane quasi-component (C14:763H31:526) leads to under-prediction of the evaporation time by about 35% which is not acceptable even for qualitative analysis of the process. In the case when n-dodecane is chosen as the single alkane component, the above-mentioned under-prediction increases to about 44%

Observational constraints on the types of cosmic strings

This paper is aimed at setting observational limits to the number of cosmic strings (Nambu-Goto, Abelian-Higgs, semilocal) and other topological defects (textures). Radio maps of CMB anisotropy, provided by the space mission Planck for various frequencies, were filtered and then processed by the method of convolution with modified Haar functions (MHF) to search for cosmic string candidates. This method was designed to search for solitary strings, without additional assumptions about the presence of networks of such objects. The sensitivity of the MHF method is $\delta T \approx 10 \mu K$ in a background of $\delta T \approx 100 \mu K$. The comparison of these with previously known results on search string network shows that strings can only be semilocal in an amount of $1 \div 5$, with the upper restriction on individual strings tension (linear density) of $G\mu/c^2 \le 7.36 \cdot 10^{-7}$. The texture model is also legal. There are no strings with $G\mu/c^2 > 7.36 \cdot 10^{-7}$. However, comparison with the data for the search of non-Gaussian signals shows that the presence of several (up to 3) of Nambu-Goto strings is also possible. For $G\mu/c^2 \le 4.83 \cdot 10^{-7}$ the MHF method is ineffective because of unverifiable spurious string candidates. Thus the existence of strings with tensions $G\mu/c^2 \le 4.83 \cdot 10^{-7}$ is not prohibited but it is beyond the Planck data possibilities.Comment: 15 pages, 10 figures; accepted by the European Physical Journal

Gravitational strings. Do we see one?

I present a class of objects called gravitational strings (GS) for their similarity to the conventional cosmic strings: even though the former are just singularities in flat spacetime, both varieties are equally "realistic", they may play equally important cosmological r\^ole and their lensing properties are akin. I argue that the enigmatic object CSL-1 is an evidence in favor of the existence of GS.Comment: The published version. Minor correction

Gravitational-Wave Stochastic Background from Kinks and Cusps on Cosmic Strings

We compute the contribution of kinks on cosmic string loops to stochastic background of gravitational waves (SBGW).We find that kinks contribute at the same order as cusps to the SBGW.We discuss the accessibility of the total background due to kinks as well as cusps to current and planned gravitational wave detectors, as well as to the big bang nucleosynthesis (BBN), the cosmic microwave background (CMB), and pulsar timing constraints. As in the case of cusps, we find that current data from interferometric gravitational wave detectors, such as LIGO, are sensitive to areas of parameter space of cosmic string models complementary to those accessible to pulsar, BBN, and CMB bounds.Comment: 24 pages, 3 figure

Blended E85-diesel fuel droplet heating and evaporation

The multidimensional quasi-discrete (MDQD) model is applied to the analysis of heating and evaporation of mixtures of E85 (85 vol % ethanol and 15 vol % gasoline) with diesel fuel, commonly known as “E85–diesel” blends, using the universal quasi-chemical functional group activity coefficients model for the calculation of vapor pressure. The contribution of 119 components of E85–diesel fuel blends is taken into account, but replaced with smaller number of components/quasi-components, under conditions representative of diesel engines. Our results show that high fractions of E85–diesel fuel blends have a significant impact on the evolutions of droplet radii and surface temperatures. For instance, droplet lifetime and surface temperature for a blend of 50 vol % E85 and 50 vol % diesel are 23.2% and up to 3.4% less than those of pure diesel fuel, respectively. The application of the MDQD model has improved the computational efficiency significantly with minimal sacrifice to accuracy. This approach leads to a saving of up to 86.4% of CPU time when reducing the 119 components to 16 components/quasi-components without a sacrifice to the main features of the model