### Abstract

A wide range of dynamic models, including those of heating, evaporation

and ignition processes in fuel sprays, is characterised by large differences

in the rates of change of variables. Invariant manifold theory is an effective

technique for investigation of these systems. In constructing the asymptotic

expansions of slow invariant manifolds it is commonly assumed that a limiting

algebraic equation allows one to find a slow surface explicitly. This is not

always possible due to the fact that the degenerate equation for this surface

(small parameter equal to zero) is either a high degree polynomial or transcendental. In many problems, however, the slow surface can be described in

a parametric form. In this case, the slow invariant manifold can be found in

parametric form using asymptotic expansions. If this is not possible, it is necessary to use an implicit presentation of the slow surface and obtain asymptotic representations for the slow invariant manifold in an implicit form. The results of development of the mathematical theory of these approaches and the applications of this theory to some examples related to modelling combustion

processes, including those in sprays, are presented.

and ignition processes in fuel sprays, is characterised by large differences

in the rates of change of variables. Invariant manifold theory is an effective

technique for investigation of these systems. In constructing the asymptotic

expansions of slow invariant manifolds it is commonly assumed that a limiting

algebraic equation allows one to find a slow surface explicitly. This is not

always possible due to the fact that the degenerate equation for this surface

(small parameter equal to zero) is either a high degree polynomial or transcendental. In many problems, however, the slow surface can be described in

a parametric form. In this case, the slow invariant manifold can be found in

parametric form using asymptotic expansions. If this is not possible, it is necessary to use an implicit presentation of the slow surface and obtain asymptotic representations for the slow invariant manifold in an implicit form. The results of development of the mathematical theory of these approaches and the applications of this theory to some examples related to modelling combustion

processes, including those in sprays, are presented.

Original language | English |
---|---|

Pages (from-to) | 1-17 |

Journal | Journal of Engineering Mathematics |

Volume | 114 |

DOIs | |

Publication status | Published - 7 Dec 2018 |

### Bibliographical note

This is a post-peer-review, pre-copyedit version of an article published in Journal of Engineering Mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10665-018-9976-4### Keywords

- Invariant manifold System order reduction
- spray ignition
- spray combustion

## Fingerprint Dive into the research topics of 'Parameterisations of slow invariant manifolds: application to a spray ignition and combustion model'. Together they form a unique fingerprint.

## Profiles

## Sergei Sazhin

- School of Computing, Engineering & Maths - Professor of Thermal Physics
- Advanced Engineering Centre

Person: Academic

## Cite this

Sazhin, S., Shchepakina, E., & Sobolev, V. (2018). Parameterisations of slow invariant manifolds: application to a spray ignition and combustion model.

*Journal of Engineering Mathematics*,*114*, 1-17. https://doi.org/10.1007/s10665-018-9976-4