Numerical investigation of thermal characteristics of conﬁned rotating multi-jet

– For using the swirling jet for air conditioning and heating in the premises, knowledge of the thermal characteristics is more than necessary. It is for this objective that the experimental and numerical study was realized. To conduct this study, we designed and built an experimental facility to ensure proper conditions of conﬁnement in which we placed ﬁve air blowing devices with adjustable vanes, providing multiple swirling turbulent jet with a swirl number S = 0 . 4. The jets were issued in the same direction and the same spacing deﬁned between them. This study concerned the numerical simulation of the thermal mixing of conﬁned swirling multi-jets, and examined the inﬂuence of important parameters of a swirl diﬀuser system on the performance characteristics. The experimental measurements are also realized for a conﬁned domain, aiming to determine the axial and radial temperature ﬁeld. The CFD investigations are carried out by an unstructured mesh to discretize the computational domain. In this work, the simulations have been performed using the ﬁnite volume method and FLUENT solver, in which the standard k - ε , K - ε realizable, k - ε RNG and the RSM turbulence model were used for turbulence computations. The validation shows that the K - ε RNG model can be used to simulate this case successfully.


Introduction
The confined multiple rotating jets were used in several industrial applications.They are very important practical interest in the technology of air conditioning systems, cooling and combustion.The rotating jet enhances mixing processes and mass and heat transfer and causes a change in the mean flow such as the properties of the turbulence.Under the effect of turbulence, the fluid particles have a tendency to move away from the axis under the effect of centrifugal force.
Depending on the literature, there is no more research being done, on the multiple rotating jets applied to improve comfort conditions.Most of the literatures which deal with multiple rotating jets in various geometric or dynamic and thermal conditions are aimed to the improvement of combustion.Swirl flows have been widely used in combustion systems as they enhance mixing between fuel and oxidant [1,2].Practically, they are found in aircraft combustors and in a burner where swirl contributes to improve mixing and stabilizes the flame.They are also a Corresponding author: Roudane moh@yahoo.frwidely used in industrial burners or gas turbine combustors to give stable, high intensity, short flames with wide radial development resulting from good fluid mixing [3].Consequently, it is worth noting that, there are still many points to be clarified concerning the understanding of the effect of rotating jet on the heat transfer and behavior of the armature flow.It has been noted that from a certain intensity of swirl, a recirculation zone appeared in the main flow.The form and position of the recirculation zone will vary with the intensity of the swirl [2][3][4][5].This area is essential to stabilize the combustion because it contains fresh gas preheated and allows the attachment of the flame.The velocity profiles of a low swirling flow (S < 0.5) takes a Gaussian form and from approximately S = 0.6, the longitudinal pressure gradients are not sufficient to compensate for the kinetic energy of fluid particles so appears a toroidal recirculation zone in the flow [2].Thielen et al. [6] presented the numerical simulation of flow and heat transfer in multiple jets impinging normally on a flat heated surface, obtained with a new second-moment turbulence closure combined with an elliptic blending model of non-viscous wall blocking effect.and turbulent stress fields in very good agreement with PIV measurements.They explored a number of simpler closures for the passive thermal field, conducted in parallel and they confirmed that the major prerequisite for the correct prediction of the temperature field and heat transfer is to calculate accurately the velocity and stress fields.
Rady [7] presented a study to determine the characteristics of flow and heat transfer of an impinging multi jet used for cooling of a flat plate equipped with exhaust ports in confinement.The experiments were realized taking into consideration the different values of Reynolds, the distance between the plate and the jet and the positioning of the exhaust ports.Points drawn from this work are listed below: -Increasing the rate of heat transfer is relative to the decrease of the distance between the plate and the jet.Acceleration of the flow, at the approach of the scattering surface of the jets, excites relatively heat transfer in the downstream.-Positioning of the jets of exhaust ports contributes to the structural change of the flow rate and the reduction of the interaction between the inflow and the outflow.
Bouziane et al. [8] studied numerically a reactive flow generated downstream swirler, three turbulence models: RNG K-ε, standard K-ε and realizable K-ε.They deduced from this study that the superposition of the graphs showing the profiles of the radial component of the axial velocity and the temperature can be an acceptable value for the study of the recirculation zone in a combustion chamber.According to Braikia et al. [9] the optimization of parameters for instance the geometry of the diffuser, the slope of the initial speed (number of swirl), the gap between jets, the number of jets blown, the inclination of the jets relative to the lateral central axis of the jet, the jet flow relative peripheral and central jet, can significantly improve the quality of air in mixtures of local cooling or gas containments.According to Aroussi et al. [10] the models realizable K-ε, the standard K-ε, RSM and RNG K ε-suited for the simulation of multiple turbulent jets in burners.From the standpoint economy in computation time, the model realizable K-ε is more suitable than the other models.Elbanna et al. [11] visualized the interaction of two-dimensional air jets, distributed, parallel, impacting on a flat surface for use in aircraft vertical takeoff and landing.They visualize the effect of the drive around the blasting orifices.Confluent jets ventilation at x/D is greater than unventilated.The rectangular holes reduce suction vortex better than round jets.They establish the distribution of the pressure fields through the confluence of the jets.The influence of turbulence is important near the side of the jet "weakest".Kazuya et al. [12] carried out a 3D numerical simulation to study the effects of swirl and buoyancy driven flows on the mixing performance of a baffle-plate-type miniature confined multi jet.According to authors the rotating flow was created by inclining the jet nozzles surrounding the central jet in the circumferential direction.The results achieved were compared with those of the non-swirl case.They found that the rotating flow interrupted the radial secondary flow produced in the region adjacent to the baffle plate.
According to Kazuya et al., this interruption decreased the size of the reverse flow region, resulting in a deterioration of the mixing performance.They noted that this performance was more perceptible in the case of a large swirl number.Hirai et al. [13] studied the numerical prediction of flow characteristics and retardation mixing in a turbulent rotating flow.They used two coaxial flow behaviors and propose two turbulence models: K-ε model and stress-flow by noting that: -The axial velocity U retains the radial profile depressed near the central axis at the downstream region in the rotating flow.-The tangential velocity W becomes the solid body rotational profile near the central axis and the free vortex profile at the outer region.
They conclude that there is concordance between the predictions of the proposed models and experimental results used.
Our objective is to experimentally measure the temperature field with a radial and axial multi rotating jet confined within a chamber leading to a flat wall for several distances from a diffuser pitch changing and to compare these results with those obtained numerically by testing different models of turbulence to validate the model for this type of configuration.

Experimental setup and techniques
The experimental setup is represented in Figure 1.It composed of a chassis on which is fixed a square Plexiglas plate with dimensions (1.20 m × 1.20 m × 2 m) On the latter, five devices blowing hot air (hairdryer-type TEFAL 1500, amended) are fixed and directed downwards, and the lower part of these devices is used to fix different types of diffusers provided with inclined vanes, depending on the studied configuration.Temperatures and velocity of the flow are measured by a thermo-anemometer (Type General Tools Digital Multi-Thermometer) which is a high-precision multifunctional instrument.The accuracy is of order ±0.5 • C for temperature from thermal sensor.Note that the thermal sensor is supported by rods which are easily guided vertically and horizontally to sweep the maximum space in the axial and radial directions (Fig. 1).
The rotating jet is obtained by swirling generator device realized for this study.This device, placed just at the exit of the cylindrical conduit of devices blowing hot air, is composed of inclined vanes fixed on polyamide support.The vanes form an angle (α) of 30 • with the axis of the jet.
The swirling confined jet treated here is different from the conventional jet because of the existence of a tangential component velocity.To attain this type of flow, one can either use the axial fan impeller for generating rotating turbulent flow, or use swirling mechanical systems [14].For example, this system includes inclined vanes, Figures 2a and 2c, which is put in the generating tube jet, Figure 2b.The application of a tangential velocity component to the flow (W ) provides a rotation to flow fluid, which is indicated by a so-called swirl number (S).This number is defined as the ratio of the axial flux of tangential momentum to the product of the axial momentum flux and a characteristic radius [15].It should be noted that the exact expression of swirl number depends on the injector geometry and flow profiles.Following Gupta [15], and for a typical single element injector with a flat vane swirler, the swirl number can be defined as: where G ∅ is the axial flux of tangential momentum, G x the axial momentum flux, and R a characteristic radius.R n and R h are radius of the centre body and the inlet duct, respectively.It is important to note here that if the axial and azimuthally velocities are assumed to be uniform and the vane are very thin, the swirl number can be written as [16]: where ∝ is the swirler vane angle.In our experiment, we must ensure that the flow is confined and good insulation from the outside during the experiments.The values of the flow initial temperature T i and the values of the ambient temperature Ta have been measured by the temperature sensors; they are identified only when the temperatures are stabilized, the delay of ten minutes is sufficient to achieve this stabilization.After the temperatures measure is realized, we stopped the blowing apparatus then we proceed to the displacement of the rods carrying the probes for other measure points.The axial and radial flows are checked to using a level.The configuration performed to guide this experimental study is shown in Figure 3.
To accomplish our experiments the flowing operating conditions were regarded: S = 0.4, Q m = 0.012 kg.s −1 , R e0 = 16 × 10 3 , the initial temperature of blown jets at the exit orifice was 92 • C and the initial axial velocity was fixed at 6 m.s −1 .

Mathematical formulation and numerical method 3.1 Mathematical formulation
The turbulence models are available in FLUENT code.The present work is based on four turbulence models: the model (k-ε) standard, RNG k-ε model, realizable k-ε and Reynolds stress model (RSM).
For a steady, three-dimensional, incompressible, and turbulent flow with constant fluid properties, the governing equations of conservation of mass, momentum and energy are written in the cartesian tensor notation as follows: where U i and T denote the mean velocity and temperature; u i , u j and T are the corresponding fluctuation components; −ρu i u j and −ρC p u i T are the average Reynolds stresses and turbulent heat fluxes which need to be modeled to close the equations.The Boussinesq hypothesis relates the Reynolds stresses to the mean velocity gradients as seen in the equation below [17]: where k is the turbulent kinetic energy, as defined by k = 1 2 u i u i , and δ ij is the tensor identity.An advantage of the Boussinesq approach is the relatively low computational cost associated with the computation of the turbulent viscosity μ t .A disadvantage is that it assumes μ t is

Numerical predictions
The geometry considered here, is a confined chamber of dimensions 1.The algorithms PRESTO and SIMPLE have been used for pressure interpolation and coupling of pressure and velocity, respectively.The numerical simulation has been performed with a triangular and unstructured mesh composed of 1 798 763 cells.A more detailed discretization was used close to the inlets of diffuser and to the axis to give high resolution where required and to save the computational effort and time calculation.Tests with finer grids (up to 2 000 000 cells) demonstrate that the quality of the prediction is not improved by enhancing the number of cells used.At the inlet the turbulence intensity is set equal to 7% with a hydraulic diameter equal to 0.17 m.The boundary conditions were used with smooth walls and without heat transfer.

The grid effect
The geometry definition and mesh generation were performed using a grid generator "GAMBIT".More refinement areas near the jet exit were taken into account to capture different phenomena that can occur in these areas, including temperature (Fig. 4).In Figure 5, the mesh effect was done by testing the RNG k-ε turbulence model for the radial temperature.

Temperatures distribution
In this section we present the experimental and numerical results which are obtained by the temperature dimensionless expression as follows: T r = [T − T a ]/[T 0 − T a ], r/D and x/D respectively, where T is the jet temperature, T a is the ambient temperature and T 0 is the maximum temperature of the air blowing at origin.The radial and axial locations are given by reference to the diameter of the blowing orifice in dimensionless form r/D 1 to 10 and x/D = 1 to 20.
The comparison of the calculated radial temperature profiles with the experimental results is given in Figure 6.We can noted that for station x/D = 1, the temperature reaches its maximum near the center line, and then decreases in away from this area until it stabilizes from r/D = 3.In the station x/D = 5, we can see that the temperature increases to its maximum near the point r/D = 1, then it starts to decrease rapidly to the point r/D = 3 and it stabilized after a low temperature variation.The increase in temperature between the r/D = 0 and r/D = 1 is due to the design of the swirler, because the periphery of the blow port is hotter than the center there of that justify the low temperature at the center of the jet.In the stations x/D = 9, x/D = 15, x/D = 18 and x/D = 20, we note that the temperature profiles are generally in the same profiles.Generally, there is a low temperature homogenization near the inlet orifice and also at station x/D = 5.
From the axial temperature profiles given in Figure 8 and the radial profiles shown in Figure 6, we can conclude that the interaction of jets reduces the amplitude of the axial temperature, while ensuring a significant spread radial temperature.Therefore there is an increase of the radial turbulence intensity.The homogenization of temperature is almost perfect; confinement improves the quality of temperature stratification along the jet.There is also an axial uniform temperature at all stations studied (Fig. 8).Temperature profiles provided thermal stability and remarkable spread.By analyzing Figure 9, we see that the number of peripheral jets ensures a more homogenization compared to a single swirling jet.
For this jet configuration, it could seem interesting to examine the changes made by different turbulence models.An examination of Figures 7 and 8, which show the temperature profiles at several radial and axial distances, shows that the difference in the numerical solution is really minimal.
The temperature profiles obtained with different turbulence models and mesh refinements are compared to the experimental data.We can see that the RNG k-ε model gives the best overall results with an average error of 4.5% with the experimental (Fig. 7).The realizable K-ε model is also achievable to obtain a reasonable prediction away from the jet axis; on the contrary, the RSM model gives a prediction acceptable near the jet axis.

Conclusion
This study showed the following results: -The use of a multiple swirling jet provides temperature profiles fairly regular, and therefore significant thermal homogenization.-In the radial direction, the temperature is more important for the multiple swirling jets that for the single swirling jet.-Confinement improves the quality of temperature stratification along the jet.-The temperature decreases less rapidly compared to a single swirling jet.-The multiple swirling jets provide in all cases, for a given station a better thermal stability and a significant growth compared to a swirling single jet.All these features show the importance of the application of this type of jet in heating and space cooling compared to conventional jet system.We can also conclude that the RNG K-model is valid for the prediction of low turbulent swirling jets, it can better predict the flow compared to other models.The model presented for excessive levels of turbulent diffusion.Note that it gives a correct representation of flow characteristics by comparing these results with experimental data.
To operate virtually results of this work with a view to their application delivery devices in air ventilation systems, it is recommended to also determine the velocity profiles of the different configurations of the jets, the pressure distribution, heat exchange and the influence of the geometry and positioning of the discharge openings on the thermal homogenization.
2 m × 1.2 m × 2 m.The air jet is heated to 92 • C and injected by five blowing devices into the chamber with circular cross section (D−d = 0.035 m) with mean axial velocity exceeding 6 m.s −1 .The air is treated as an incompressible fluid and Newtonian.The FLUENT computer code uses a finite volume procedure to solve the Reynolds averaged Navier-Stokes equations (RANS) of fluid flow.A choice of solution methods and turbulence are available in this CFD code.The models used for the numerical calculation are as follows: for turbulence, k-ε model, RNG k-ε model, realizable k-ε and the Reynolds Stress Model (RSM) model with the axisymmetric swirl option (S = 0.4) are used.The numerical prediction has been carried out with the following assumptions: the flow is steady three dimensional axisymmetric and turbulent.

Fig. 7 .
Fig. 7. Histogram of errors quantification between numerical and experimental results.

Fig. 8 .
Fig. 8.Comparison of the axial temperature distribution of the multiple swirling jet with the experimental results.

Fig. 9 .
Fig. 9. Comparison of axial temperature profiles of single and multiple swirling jet (experimental results).