In this work, entropy generation analysis is applied to characterize and optimize a turbulent impinging jet on a heated solid surface. In particular, the influence of plate inclinations and Reynolds numbers on the turbulent heat and fluid flow properties and its impact on the thermodynamic performance of such flow arrangements are numerically investigated. For this purpose, novel model equations are derived in the frame of Large Eddy Simulation (LES) that allows calculation of local entropy generation rates in a post-processing phase including the effect of unresolved subgrid-scale irreversibilities. From this LES-based study, distinctive features of heat and flow dynamics of the impinging fluid are detected and optimal operating designs for jet impingement cooling are identified. It turned out that (1) the location of the stagnation point and that of the maximal Nusselt number differ in the case of plate inclination; (2) predominantly the impinged wall acts as a strong source of irreversibility; and (3) a flow arrangement with a jet impinging normally on the heated surface allows the most efficient use of energy which is associated with lowest exergy lost. Furthermore, it is found that increasing the Reynolds number intensifies the heat transfer and upgrades the second law efficiency of such thermal systems. Thereby, the thermal efficiency enhancement can overwhelm the frictional exergy loss.

To cope with the progressive tightening of the emission regulations, gasoline and diesel engines will continuously require highly improved exhaust after-treatment systems. In the case of diesel engines, the selective catalytic reduction (SCR) appears as one of the widely adopted technologies to reduce NO_x (nitrogen oxides) emissions. Thereby, with the help of available heat from exhaust gas, the injected urea–water solution (UWS) turns inside the exhaust port immediately into gaseous ammonia (NH₃) by evaporation of mixture and thermal decomposition of urea. The reaction and conversion efficiency mostly depend upon the evaporation and subsequent mixing of the NH₃ into the exhaust gas, which in turn depends upon the engine loading conditions. Up to now, the aggregation of urea after evaporation of water and during the thermal decomposition of urea is not clearly understood. Hence, various scenarios for the urea depletion in the gaseous phase that can be envisaged have to be appraised under SCR operating conditions relying on an appropriate evaporation description. The objective of the present paper is therefore fourfold. First, a reliable multi-component evaporation model that includes a proper binary diffusion coefficient is developed for the first time in the Euler–Lagrangian CFD (computational fluid dynamics) framework to account properly for the distinct evaporation regimes of adBlue droplets under various operating conditions. Second, this model is extended for thermal decomposition of urea in the gaseous phase, where, depending on how the heat of thermal decomposition of urea is provided, different scenarios are considered. Third, since the evaporation model at and around the droplet surface is based on a gas film approach, how the material properties are evaluated in the film influences the process results is reported, also for the first time. Finally, the impact of various ambient temperatures on the adBlue droplet depletion characteristics as well as the effect of gravity is pointed out. The prediction capability of the model variants is assessed by comparing the achieved results to each other and with experimental data. It turns out that satisfactory agreement between experiment and numerical predictions is achieved for a wide range of operating temperatures by using correlations by “Wilke and Lee” for urea and by “Fuller et al.” for water. The results are essentially sensitive to gravity. From subsequent comparisons of different ways to account for the thermal decomposition in the gaseous urea, a significant difference is observed. Finally, the 1/3 film rule widely used for evaluating the material properties in the film shows accurate prediction of both evaporation and thermal decomposition regimes of urea.

The quantification of the prediction accuracy in large eddy simulations (LES) is very challenging due to various interacting errors associated with this approach. When dealing with errors in LES using implicit filtering, numerical and modeling errors have drawn the interest of many researchers. Little attention has been paid to other sources of discrepancies between LES results and reference data, namely sampling errors, influence of the initial conditions, improper boundary conditions or uncertainties issuing from reference data. A framework of metrics that includes all these issues is addressed in the present paper to study subgrid-scale (SGS) models for LES and to quantify their prediction accuracy and computational costs. The method is applied to a simple wall-bounded turbulent flow at moderate Reynolds number. It turns out from the results obtained with six commonly used SGS models that wall-adapting models (WALE and SIGMA) and localized dynamic models reproduce the physics of the flow field more faithfully, reveal a superior prediction accuracy and have a similar computational cost than models using van Driest wall damping. Especially at the viscous wall region (\(r^+<50\)), wall-adapting and localized dynamic models are more accurate, reflecting the proper near wall behavior of such models. Relying on the analysis of sources of various errors, uncertainties in LES are estimated and systematically assessed, and their influence on simulation results is quantified. Finally, engineering estimations of the required averaging time to obtain basic estimates of statistical quantities with a predetermined degree of accuracy are suggested.

In this work, near-wall thermal transport processes and entropy generation mechanisms in a turbulent jet impinging on a ${45}^{\circ }$ -inclined heated surface are investigated using a direct numerical simulation (DNS). The objectives are to analyze the subtle mechanisms of heat transport in the vicinity of an inclined impinged wall, to determine the causes of irreversibilities that are responsible for the reduction of performance of impingement cooling applications and to provide a comprehensive dataset for model development and validation. Results for near-wall thermal characteristics including heat fluxes are analyzed. An entropy production map is provided from the second law analysis. The following main outcomes can be drawn from this study: (1) the location of peak heat transfer occurs not directly at the stagnation point; instead, it is slightly shifted towards the compression side of the jet, while at this region, the heat is transported counter to the temperature gradient; (2) turbulent thermal and fluid flow transport processes around the stagnation point are considerably different from those found in other near-wall-dominated flows and are strongly non-equilibrium in nature; (3) heat fluxes appear highly anisotropic especially in the vicinity of the impinged wall; (4) in particular, the heated wall acts as a strong source of irreversibility for both entropy production related to viscous dissipation and to heat conduction. All these findings imply that a careful design of the impinged plate is particularly important in order to use energy in such a thermal arrangement effectively. Finally, this study confirms that the estimation of the turbulent part of the entropy production based on turbulence dissipation rates in non-reacting, non-isothermal fluid flows represents a reliable approximate approach within the second law analysis, likewise in the context of computationally less expensive simulation techniques like RANS and/or LES.