https://orcid.org/0000-0002-7700-745X
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ABSTRACT
The fuel injection and mixing process are often carried out under trans-/supercritical conditions for engine applications; however, the process is still unclear. In this study, based on OpenFOAM, a multi-component trans-/supercritical spray model based on the KT/KNP scheme is developed, which covers the special real fluid equation of state, various mixing rules and modified thermodynamic properties. In addition, the PIMPLE algorithm is extended to deal with the high nonlinearity. First, a one-dimensional advection case is applied to evaluate the performance of the model. Then, the effect of various mixing rules and pseudo-boiling phenomenon on n-heptane/nitrogen jet are thoroughly analyzed under trans-/supercritical conditions. The results show that the jet is extremely sensitive to the changes of the initial jet temperature and chamber pressure, and the “heat shield” effect of pseudo-boiling delays the breakup and mixing in the transcritical jet. With the mixing of different components, unlike the single-component condition, the pseudo-boiling intensity will increase. The increase of pressure and occurrence of mixing will lead to the decrease of pseudo-boiling temperature, and the pseudo-boiling will end earlier, which is obviously different from the single-component fluid case. For the n-heptane/nitrogen mixture, when the mole fraction of n-heptane in the mixture changes from 1.0 to 0.7, and the pseudo-boiling temperature decreases from 571 K to 465 K. With increasing injection temperature or chamber pressure, the pseudo-boiling intensity gradually decreases, and the potential core shortens, the difference among various mixing rules decreases. When the injection temperature is higher than 571 K, the pseudo-boiling phenomenon no longer exists. When the chamber pressure reaches 9 MPa, the pseudo-boiling strength is very low. Therefore, the spray mixing under supercritical conditions will be more sufficient. With the occurrence of mixing, the critical parameter gradually transitions from the critical value of n-heptane to the critical value of nitrogen, which strongly depends on the mixing rule.
Acknowledgements
The authors gratefully acknowledge the financial support from theNational Natural Science Foundation of China(51576029, 51606176).
Disclosure statement
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Nomenclature
| AP | = | coefficient matrix |
| Cp | = | constant pressure specific heat, J·kg−1·K |
| cf | = | local speed of sound, m·s−1 |
| D | = | material derivative |
| Di,m | = | effective mass diffusion coefficient |
| Dij | = | binary diffusion coefficient |
| h | = | specific enthalpy, J·kg−1 |
| ht | = | total enthalpy, J·kg−1 |
| Ji | = | mass diffusion flux of species i |
| M | = | molecular weight, kg·mol−1 |
| Ma | = | local face Mach number |
| Nc | = | number of species |
| p | = | pressure, Pa |
| Pc | = | critical pressure, Pa |
| Ru | = | universal gas constant, J·kg−1·K−1 |
| Sf | = | surface normal vector |
| T | = | temperature, K |
| Tc | = | critical temperature, K |
| u | = | velocity vector, m·s−1 |
| v | = | specific volume, m3·kg−1 |
| vc | = | critical volume, m3·kg−1 |
| Xi | = | mole fraction of species i |
| Yi | = | mass fraction of species i |
| Zc | = | critical compressibility factor |
| Greek Symbols | = | |
| αeff | = | effective thermal diffusion coefficient |
| ϕf | = | face volume flow rate |
| ρ | = | mixture density, kg·m−3 |
| ω | = | acentric factor |
| μ | = | dynamic viscosity, pa·s |
| τ | = | viscous stress tensor, m2·s−2 |
| λ | = | thermal conductivity, W·m−1·K |
| kij | = | binary interaction parameter |
| φ | = | isothermal compressibility |
| Subscripts | = | |
| f | = | face |
| i | = | species |
| m | = | mixture |
| n | = | current time step |
| n-1 | = | previous time step |
| ij | = | specific off-diagonal element |
| ref | = | reference value |
| Superscripts | = | |
| 0 | = | ideal reference state |