Flow Asymmetry in Symmetric Multiple Impinging Jets : A Large Eddy Simulation Approach

A numerical study on in-line arrays of multiple turbulent round impinging jets on a flat heated plate was conducted. The Large Eddy Simulation turbulence model was used to capture details of the instantaneous and mean flow fields. The Reynolds number, based on the jets diameter, was equal to 20,000. In addition to flow features known from single jets, the interaction between the neighboring jets was successfully elucidated. Symmetry boundary conditions were imposed to reduce the computational domain to only a quarter. In accordance with previous numerical and experimental works, the asymmetry in the velocity field near to the impingement plate was also found to exist. LES showed oval imprints of the Nusselt number similar to experiments but with some discrepancies on the symmetry boundaries. The asymmetry, observed in previous experimental and numerical results, in the horizontal planes, parallel and close to the impingement wall, was confirmed. The recirculation zone responsible for asymmetry, known to develop due to the wall jets interaction, was seen in only one side of the diagonal formed by the central and the farthest jets.


Introduction
The present paper reports on Large Eddy simulation (LES) of multiple turbulent round impinging jets on a heated flat plate.Because of the high heat transfer rates that can be achieved using them, impinging jets _________________________________________ *Corresponding author's e-mail: lkhezzar@pi.ac.ae are employed in a wide range of important industrial applications for cooling, heating, and drying solid obstacles or paper and textiles with different shapes, cooling of electronics components, and annealing of steel.
Single impinging jets have been extensively studied (Yokobori et al. 1977;Hadžiabdic and Hanjalic 2008) and the turbulent flow and the heat transfer they induce are well elucidated.Nonetheless some features are still being investigated such as the Nusselt number dip and second peak observed for small jet-slot-toimpingement distances.The parameters affecting single impinging jets flow behaviour are: the Reynolds number, the slot shape, the slot-to-impingement distance, and the impingement obstacle shape.The Multiple impinging jets represent an extension of the single jet where more complex phenomena take place.The interaction of the jets generates secondary flows in the space separating the jets depending on their distribution and pitch in addition to the other parameters mentioned for the single jet case.Impinging jets create also horizontal wall jets along the impingement surface which , impact at a certain distance from the impingement region.The impact causes the wall jets to deviate in an uplift motion then to be entrained downward by the free jets.Thus, recirculation zones are created in the corners formed by the free and the wall jets.Garimella and Schoeder (2001) have studied the local heat transfer distributions for three different configurations of in-line jet arrays compared with a single jet.They noticed that the central jet in the ninejet array generated a higher heat transfer coefficient at the stagnation point in comparison with the single jet at the same Reynold number.Thielens et al. (2003) have conducted a simulation work on in-line and circular impinging jets using the kand v 2 -f turbulence models and latter on using a modified secondmoment-closure model (Thielen et al. 2005).They have considered a quarter of the real domain relying on symmetry boundary conditions.Their results showed, surprisingly for the in-line jets configuration, an asymmetry of the flow along the diagonal axis.Geers et al. (2006), in their experimental work, have confirmed the existence of the asymmetry noticed in Thielen's works thereby demonstrating that it was not a CFD artifact.In addition they have studied a hexagonal configuration of multiple jets with sharp-edged and contoured jet-outlet-orifices.The Reynolds averaged Navier-Stokes (RANS) equations and corresponding turbulence models are still being used due to their reasonable computational-tools requirements.Xing et al. (2010) have compared the performance of in-line and staggered jets under the effect of variable crossflow regimes.They used the Shear Stress Transport (SST k-) turbulence model (Menter 1994).They found that the in-inline configuration yielded better heat transfer rates.The SST k-appears to be the best RANS model for predicting multiple jets flows as stated by Spring et al. (2010).Indeed, they used it to investigate the heat transfer occurring during the process of cooling combustor liner heat shield.The slots were irregularly distributed.They noticed that the numerical simulation over-predicted the Nusselt number at the impingement point by up to 100% with an average error of 40%.
Large eddy simulation allows the resolution of large energetic scales of motions whereas the small dissipative scales are modeled through a sub grid model.It thus captures more flow details compared to the classical RANS models and offers a viable alternative for computing industrial flows between RANS on the one hand and direct numerical simulations (DNS) which require intensive resources on the other.To the authors knowledge no LES predictions for this type of flow have been reported before.In the present work the LES turbulence model is used to predict the turbulent flow and heat transfer features of in-line multiple round impinging jets to find out if the flow asymmetry is still present and discuss the correlation between flow and heat transfer from instantaneous flow properties.It is seen that LES captures the interaction between the adjacent jets and their effects on heat transfer with very good accuracy.The numerical results obtained are validated based on the detailed experimental work of Geers et al. (2006).

Geometry and Computational Grid
The configuration studied corresponds to the in-line arrays of jets of the experimental work done by Geers et al. (2006).The geometry and relevant dimensions and orientation are shown in Fig. 1.Each jet nozzle has a diameter D = 13 mm.The nozzles-to-impingement distance H and the pitch S are both equal to 4D.Based on an inlet velocity of 23.88 m/s and air properties at room temperature, the Reynolds number for each jet is 20,000.A multi-bloc hexahedral mesh of about 9.5 million computational cells was generated (Fig. 2).Only one quarter of the domain has been considered in the present simulation work relying on symmetric boundary conditions.Thus, only four among the nine jet nozzles located on a solid plate are represented in Fig. 2. The mesh was refined in the regions where high gradients were expected which are, the free-shear layer developing from the orifice contour and the wall jet layers near the two walls.
The non dimensional distance y+ was inferior to 1.8 on the lower wall and to 7 in the upper wall.

Mathematical Formulation
The fluid is assumed incompressible and the filtered continuity and momentum equations solved are given by: (1) (2) where the variables with an over bar represent the filtered (the locally averaged) values.The laminar stress tensor is given by: (3) The subgrid stress accounting for the unresolved scales contribution is defined by: (4) It is modeled using the Boussinesq hypothesis The turbulent Prandtl number is estimated by applying the dynamic procedure to the subgrid-scale flux (see Germano et al. 1991, Lilly 1992).

Boundary Conditions, Discretization, and Simulation Strategy
Figure 1 illustrates the boundary conditions used.Uniform velocity profiles were imposed at the inlet with a turbulence intensity of 0.8%.The fluctuating velocities were generated using the spectral synthesizer (Kraichnan 1970, Smirnov et al. 2001).The temperature at the inlet was set to 299 K.No slip condition was used for the upper wall with a constant temperature equal to that of the inlet.At the impingement wall, no slip condition was imposed in conjunction with a constant heat flux of 1562.5 W/m 2 .For the out-  et al. 2010) that the RANS turbulence of the wall jets resulting from the deviated jets after impinging on the heated wall and, hence, is highly unstable and consequently a local enhancement of the heat transfer nearby is most probable.

Effect of the Flow Field on the Heat Transfer
To investigate the effect of the flow on the heat transfer contours of the mean pressure, the turbulent kinetic energy, the mean temperature, and the average Nu are plotted on or close to the impingement wall in Figs.9-12.Figures 9 and 10 show that the mean temperature and the average Nu have identical imprints since the Nu is proportionally dependent on the temperature.
In Fig. 11, the imprint of the mean pressure contours, resulting from the forces exerted by the jet flow on the impingement wall, appears to have a similar shape to that of the average Nu.Indeed, oval imprints Figures 13 and 14 illustrate the interaction of the x/D=0) and the impingement wall are y/D=0 and /D=4), it can be seen that the well-known Reynolds Nu maxima coincide with jet.They related the high peaks of the Nusselt number and the friction coefficient, around and far from the impingement point, to the impact of the large-scale eddy structures which, according to them, play a key role in heat transfer.The use of symmetry boundary conditions, for such flows, has been found realistic far from the impingement wall where the mean and the turbulent flow features were accurately captured.Close to the boundary where symmetry was imposed, acting as a wall, the jet flapping was artificially suppressed.This lead to the generation of recirculation zones in the corner formed by the impingement wall and the symmetry boundary.The recirculation zones acted as an obstacle to the free jets preventing them from directly impinging on the flat plate resulting in somewhat unrealistic behaviour of the flow and heat transfer close to the impingement region.
Karman constant, d is the closest C S is the Smagorinsky constant et V is the volume of the com-