This paper focuses on a wall-resolved Large Eddy Simulation (LES) of an isothermal round submerged air jet impinging on a heated flat plate, at a Reynolds number of 23 000 (based on the nozzle diameter and the bulk velocity at the nozzle outlet) and for a nozzle to plate distance of two jet diameters. This specific configuration is known to lead to a non-monotonic variation of the temporal-mean Nusselt number as a function of the jet center distance, with the presence of two distinct peaks located on the jet axis and close to two nozzle diameters from the jet axis. The objectives are here twofold: first, validate the LES results against experimental data available in the literature and second to explore this validated numerical database by the use of high order statistics such as skewness and probability density functions of the temporal distribution of temperature and pressure to identify flow features at the origin of the second Nusselt peak. Skewness (Sk) of the pressure temporal distribution reveals the rebound of the primary vortices located near the location of the secondary peak and allows to identify the initiation of the unsteady separation linked to the local minimum in the mean heat transfer distribution. In the region of mean heat transfer enhancement, joint velocity-temperature analyses highlight that the most probable event is a cold fluid flux towards the plate produced by the passage of the vortical structures. In parallel, heat transfer distributions, analyzed using similar statistical tools, allow to connect the above mentioned events to the heat transfer on the plate. Thanks to such advanced analyses, the origin of the double peak is confirmed and connected to the flow dynamics. Published by AIP Publishing.
In an attempt to improve our understanding of the fundamental flow problem that is an impinging jet, a wall-resolved Large Eddy Simulation (LES) is produced to investigate large-scale unsteady flow features, mixing processes near the wall and heat transfer. The simulation focuses on a single unconfined round jet normally impinging on a flat plate at a Reynolds number (based on the pipe diameter and bulk velocity) of Re = 23 000 and for a nozzle to plate distance of H = 2D. This configuration is known to lead to a double peak in the Nusselt distribution. Evaluation of the high order statistics, such as Skewness and Kurtosis of the temporal evolution of axial velocity and wall heat flux, provides first-ever insights into the effect of the vortical structures on the mean wall heat transfer. Heat transfer statistics such as probability density functions (PDF) confirm the ability of LES to reproduce the strong intermittent thermal events responsible for the increase of the mean wall heat transfer radial distribution. Axial velocity and temperature temporal distributions are analysed simultaneously to gain further insight into the mixing process near the wall. In particular, the probabilities of the different cold/hot fluid ejection/injection events prove that the strong intermittent thermal events are linked to a change in the mixing behavior induced by the passage of the large-scale vortical structures. These structures are found to preferentially produce a cold fluid flux towards the wall leading to the local heat transfer enhancement usually identified by the secondary peak.
One of the state-of-the-art system for turbine blade trailing edge cooling consists in blowing air, coming from the internal cooling system of the blade, through slots over a cutback on the pressure side. To increase the stiffness, this cutback is commonly equipped with internal ribs. The classical RANS method is widely used in industry to design such a system. However, it has been shown that the accuracy of such a stationary formalism is limited for the prediction of the adiabatic effectiveness due to the fact that the flow is driven by large-scale unsteadiness. In this context, Large Eddy Simulation (LES) appears as a good alternative to improve the quality of the predictions. However, the LES formalism has been scarcely used for trailing edge cooling configuration mainly because of the computational effort associated with such a problem as well as the need to deal with real complex geometries. To reduce costs, most of the time LES studies assume a periodic flow in the spanwise direction. Using this hypothesis, only one cooling passage is simulated making use of a lateral periodic boundary condition. The flow is however likely to be forced by this assumption while the side effects due to the end walls are neglected. In practice, the applicability of this periodic boundary condition has been rarely investigated in past studies. In the case of a trailing edge cutback equipped with internal ribs, there are several phenomena, e.g. coalescence of adjacent jets, which should be considered before using a lateral periodic boundary condition. In the present study, the relevance of such a periodic boundary condition is investigated. To do so, a transonic vane trailing edge equipped with a pressure side cutback and internal ribs is simulated using LES. The chosen setup was studied experimentally at DLR within the framework of the European project AITEB-2. The cooling air is blown through a channel, which is equipped with 2 rows of ribs in an inline arrangement to increase the stiffness of the thin trailing edge region. From the experimental results, it is reasonable to assume that several jets merge if looking at the adiabatic effectiveness results. Therefore, this configuration appears as a good candidate to investigate the relevance of lateral periodic boundary condition for trailing edge cutback flows. To achieve this, two LES are performed for two different computational domain sizes using lateral periodic boundary conditions. Merging of adjacent jets, expected from the experimental results, is highlighted in the simulations. This regrouping mechanism is shown to be dependent on the size of the computational domain. A strong sensitivity of the local adiabatic effectiveness to the computational domain size is highlighted while the global adiabatic effectiveness shows little sensitivity. Finally, it is shown that state-of-the-art RANS modeling is unable to reproduce correctly the local distribution of the adiabatic film effectiveness as well as the decrease of the laterally averaged effectiveness.
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