Numerical analysis of heat transfer characteristics of spray flames impinging on a wall under CI engine-like conditions

Design of Compression Ignition (CI) engines with improved thermal efficiencies needs better understanding of the heat transfer mechanism from spray flame to the combustion chamber wall. In this regard, heat transfer occurring during the interaction between impinging spray flame and wall, under CI engine-like conditions, is investigated in this study using 3-Dimensional numerical simulations based on an Eulerian–Lagrangian framework. Simulations are performed for different fuel spray injection velocities (which are representative of different fuel injection pressures in CI engines), to examine their influence on the heat transfer between impinging spray flame and wall. To couple the convective and radiative heat transfer at the wall surface with the conduction heat transfer occurring within the finite thickness wall, Conjugate Heat Transfer (CHT) is incorporated in the simulations. A Non-Adiabatic Flamelet/Progress Variable (NA-FPV) approach is employed as the combustion model of n-dodecane, which is considered to be the fuel for liquid spray. Dynamics of the liquid film formed on the wall surface by impinging fuel droplets are captured using a particle-based approach. Contribution of radiative heat flux is taken into consideration using the Discrete Ordinates (DO) method. Results indicate that the total heat flux (sum of convective and radiative heat fluxes) at the wall surface increases with the fuel injection velocity. It is observed that the total wall heat flux is largest in the stagnation zone where the spray flame impinges directly on the wall surface, while the radiative heat flux at the wall surface becomes larger as the distance from this stagnation zone increases. Additionally, it is found that the influence of fuel injection velocity on the radiative heat flow rate at the wall surface is rather small. This radiative heat flow rate when expressed as a percentage of the total wall heat flow rate, ranges from ≈ 18% to 30% (depending on the 3 cases investigated), indicating that its contribution cannot be neglected for the CI engine-like conditions under which the present simulations are performed. Furthermore, to characterize the heat transfer occurring during spray flame-wall interaction process, correlations between the Nusselt number Nu (corresponding to the wall heat loss) and Reynolds number Re (of the flow field) of the form Nu ∝ Re, are analysed and compared with that of a previous experimental study to assess their applicability. It is found that, depending on how the Nusselt number Nu is defined (either using the total wall heat flux or the convective heat flux), the value of the correlation index n changes. When Nu is calculated based on the total wall heat flux (which includes the contribution from the radiative heat flux), the value of n is found to be 0.49 which is close to the correlation index value of n = 0.4 reported in the recent experiments performed at Toyota Central R&D Labs., Inc