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Comparative Investigation on Heated Swirling JetsUsing Experimental and Numerical ComputationsAli Khelila, Hassane Najibc, Mohamed Braikiaa & Larbi Loukarfiaa Université de Chlef, Chlef, Algérieb Université d’Artois, Laboratoire Génie Civil et géo-Environnement, Béthune, Francec Université Lille Nord de France, Lille, FranceAccepted author version posted online: 25 Mar 2014.Published online: 08 Aug 2014.

To cite this article: Ali Khelil, Hassane Naji, Mohamed Braikia & Larbi Loukarfi (2015) Comparative Investigation onHeated Swirling Jets Using Experimental and Numerical Computations, Heat Transfer Engineering, 36:1, 43-57, DOI:10.1080/01457632.2014.906279

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Heat Transfer Engineering, 36(1):43–57, 2015Copyright C©© Taylor and Francis Group, LLCISSN: 0145-7632 print / 1521-0537 onlineDOI: 10.1080/01457632.2014.906279

Comparative Investigation on HeatedSwirling Jets Using Experimental andNumerical Computations

ALI KHELIL,1 HASSANE NAJI,2,3 MOHAMED BRAIKIA,1

and LARBI LOUKARFI1

1Universite de Chlef, Chlef, Algerie2Universite d’Artois, Laboratoire Genie Civil et geo-Environnement, Bethune, France3Universite Lille Nord de France, Lille, France

The purpose of this paper is to investigate both experimentally and numerically the influence of various parameters on thedifferent blowing configurations of multiple swirling jets. Flow rate was adjusted at Reynolds numbers ranging from 104

to 3 × 104. The current study is carried out under uniform heat flux condition for each diffuser, at Reynolds number of3 × 104, with air being the working fluid. Experiments concerning the fusion of several jets show that the resulting jet is clearlymore homogenized under swirling influence. Afterward, numerical simulation is also carried out using the finite-volumecomputational fluid dynamics solver FLUENT 6.3, in which the standard k − ε and the Reynolds stress turbulence model(RSM) were used for turbulence computations. The findings of this study show that the diffuser vane angle and a balance andan imbalance in temperature between the central and peripheral jets affect the quality of the thermal homogenization of theambiance. Overall predictions obtained with the RSM model are in better agreement with the experimental data comparedto those of the standard k − ε model.

INTRODUCTION

Swirling jets are widely encountered in engineering facili-ties, such as for cyclone combustors, combustion engines, tan-gentially fired furnaces, swirl burners, cleaning, and cooling andheating, among others. They are frequently used to improve heattransfer in heating and ventilation. The azimuthal motion canbe given to the jet by different mechanisms, for example, byusing inclined vanes. The understanding of swirl effects is veryimportant for the efficiency of the ventilation process. However,to our knowledge, these effects have been scarcely investigated,and consequently the fusion of many swirling jets becomes in-teresting to study. The multiple swirling free jets studies showthat swirling jets will develop more rapidly than jets without

Address correspondence to Professor Hassane Naji, Universite Lille Nord deFrance, F-59000 Lille, France; Universite d’Artois, Laboratoire Genie Civil etgeo-Environnement (EA 4515), Technoparc Futura, F-62400, Bethune, France.E-mail: hassane.naji@univ-artois.fr

Color versions of one or more of the figures in the article can be found onlineat www.tandfonline.com/uhte.

swirl. Note that the number of jets contributes to decrease ve-locities. Also, the distance between blowing orifices involves adecrease of velocities while delaying jets fusion. For high swirlnumbers and far from the orifices, velocity profiles of multiplejets have a tendency to increase compared with those of thesingle jet. The interaction between jets allows the distributionof velocities in the mixing zone in which the normal stressesand maximum shear are located. Near the origin of the swirler,the profiles are characterized by irregularities due to the swirlergeometry and the blowing conditions [1]. It should be noted thatthe axial temperature for the multijet seems to have an exponen-tial decrease [2–10]. According to the available literature, thereis no advanced research being done on the multiple swirlingjets applied to improve thermal homogenization. Most papersthat deal with multiple swirling jets in various geometric, dy-namic, and thermal conditions are aimed at the improvementof combustion [11]. Yimer et al. [12] experimentally studiedthe development of the flow from multiple-jet cold-model burn-ers. They measured the fields of mean velocity and velocityfluctuation intensity with Pitot probes. They noted that beyondthe near field, flows are virtually the same and are similar tothose of a round jet from a single source, and in the near field,

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individual structures peculiar to each burner are observed. Yin[13] experimentally investigated twin jets flow, generated bytwo identical parallel axisymmetric nozzles. He found that thetwin jets attract each other. With increasing Reynolds number,the turbulence energy grows, which indicates that the twin jetsattract acutely. He also observed that the jet flow field and themerging process of twin jets vary with the spacing betweentwo nozzles. One of his salient findings is that the width of thetwin jets flow spreads linearly downstream and grows with thespacing between two nozzles.

The effect of various parameters on flow development be-hind a vane swirler was extensively studied experimentally andnumerically by Raj and Ganesan [14]. This work highlightedthe main features of flow field generated by vane swirler. Theuniqueness of this study is in arriving at the best vane angleusing appropriate turbulence models for both weak and strongswirl. It is found that for a weak swirl, the standard k − ε modelis sufficient, whereas for strong swirl one has to resort to theReynolds stress model. In addition, they implicitly pointed outthat over the range of vane angle investigated the best vane angleis found to be 45◦.

Ahmadvand et al. [15] studied experimentally and numeri-cally the influence of the axial vane swirler on increase of heattransfer and turbulent fluid flow. Their study has been carriedout for three blade angles of 30◦, 45◦, and 60◦ with uniformheat flux condition of air, which is used as the working fluid.These authors confirmed that the use of a vane swirler leadsto a higher heat transfer compared with those obtained fromplain tubes, and the thermal performance increases as vane an-gle is raised and decreases by growth of Reynolds number.Wang et al. [16] conducted a numerical study indicating thatmultijet injection, especially four jets spaced circumferentially90◦ apart, was a favorable configuration to enhance mixing ascompared with single-jet injection, and that an even number ofopposing jets may be preferable to an odd number of opposingjets. Later, Giorges et al. [17] carried out a systematic numer-ical study for single- and multiple-jet injections into a mainstream using the standard k − ε turbulence model available inthe computational fluid dynamics (CFD) code FLUENT. Theirnumerical results displayed that multiple opposing jet injectionnot only gave better mixing but decreased power requirementswhen the number of side inlet jets increased. Suyambazhahanet al. [18] studied numerically non-isothermal twin parallel jetsin horizontal orientation to ascertain the main flow structureand the oscillation characteristics of temperature and velocityfields. Such analysis is carried out for Reynolds number be-tween 9 × 103 and 12 × 103 using the standard k − ε model.They found that the simulation results compare well with avail-able experimental data on axial velocity distribution and jetmerger distance. Wang and Mujumdar [19] studied the fluidflow and mixing characteristics of multiple and multiset three-dimensional confined turbulent round opposing jets in a novelin-line mixer using the standard k − ε turbulence model. Theyobtained a good agreement between the simulated results andexperiments.

From the literature review, it appears that vortex flows un-deniably have some advantages in terms of power mixing. Asmentioned already, all research studies conducted on such kindsof flow are somewhat remote from our present study. Thus,assessing the relevance of integrating the turbulent jets in theair handling and ventilation of living spaces and transport re-quires prior study and analysis of multijet swirling over its en-tire length. For that reason, the choice of a system consistingof blow jets more efficient in terms of mixing may be neces-sary. More recently, Escue and Cui [20] presented a numericalstudy of the swirling flow inside a straight pipe. Computationsare performed using FLUENT commercial software [21]. Theturbulent models used in that study include the RN G − k − ε

and the Reynolds stress model (RSM). They found that the lattermodel becomes more appropriate as the swirl is increased. Asmentioned before, previous studies showed that for a range ofexperimental conditions, heat transfer enhancement is stronglydependent on blade angle, and it seems that the Reynolds num-ber Re has no significant influence, whereas when the initialangle of the velocity α increases, the jet is more spreading inthe radial direction [15]. In this study, the dimensionless tem-perature and r- and x-coordinates were normalized in the formTr = (T − Ta) / (T0 − Ta), r/D, and x/D, respectively, whereT is the jet temperature, Ta is the ambient temperature, and T0

is the maximum temperature of the air blowing at origin.From the preceding discussion, the main aim of this study is

to examine the influence of various parameters such as the num-ber, the arrangements of the single or multiple swirling jets, andthe diffuser vane angle on the flow resulting both dynamicallyand thermally. In addition, we expect that parametric study ofthese parameters will help to optimize the choice of the config-uration of interest to industry and the choice of the turbulencemodel that adapts with the numerical simulation of the multipleswirling jets.

EXPERIMENTAL SETUP AND TECHNIQUES

The experimental facility is depicted in Figure 1. It consistsof a size chassis 2000 × 800 × 400 (mm), which is fixed on asquare plate of Plexiglas. On the latter, three devices blowinghot air (hairdryer TEFAL-1500) are fixed and directed down-ward, and the lower part of these devices is used to fix differenttypes of diffusers provided with inclined vanes, depending onthe studied configuration. Temperatures and velocity of the floware measured by a hot-wire anemometer (type Velocicalc PlusAir Velocity Meter [22]), which is a high-precision multifunc-tional instrument. The data can be viewed on a screen, printed,or downloaded to a spreadsheet program, allowing us to easilytransfer data to a computer for statistical treatment. The accuracyis of order ±0.015 m/s for velocity and ±0.1◦C for temperaturefrom the thermal sensor. Note that the thermal sensor is sup-ported by rods that are easily guided vertically and horizontallyto sweep the maximum space in the axial and radial directions.

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1- Air blowing Devices, 2- Diffuser with inclined vanes, 3-Thermoanemometer probe, 4- Thermo anemometer, 5-Thermometer.

4

800 mm

2D2D

5

1

2

3

r

x

2000 mm

400 mm

Figure 1 Experimental facility and test assembly.

The swirling free jet considered here is different fromthe conventional jet because of the existence of a tangentialcomponent velocity. To obtain this kind of flow, one can useswirling mechanical systems. For example, this system includesinclined vanes (see Figures 2a–2c), which are put in the gen-erating tube jet (see Figure 2b). The application of a tangentialvelocity component to the flow (W ) provides a rotation to flowfluid, which is indicated by a so-called swirl number (S). Thisnumber is defined as the ratio of the axial flux of tangentialmomentum to the product of the axial momentum flux and acharacteristic radius [23]. It should be noted that the exact ex-pression of swirl number depends on the injector geometry andflow profiles. For a typical single-element injector with a flatvane swirler, the definition of swirl number given by Guptaet al. [23] can be expressed as

S = Gθ

/RGx =

∫ Rh

Rn

U Wr2dr

/∫ Rh

Rn

RnU 2rdr (1)

where Gθ is the axial flux of tangential momentum, Gx is the

axial momentum flux, and R is a characteristic radius. Rn and

Figure 2 Schematic of swirling generator device.

Rh are radius of the center body and the inlet duct, respectively.It is important to note here that if the axial and azimuthallyvelocities are assumed to be uniform and the vanes are verythin, the swirl number can be expressed as

S = 2

3

[(1 − (

Rh/

Rn)3

)/(1 − (

Rh/

Rn)2

)]tan α (2)

where α is the swirler vane angle. Throughout the remainder ofthis paper, this parameter is called the vane angle.

Details of this expression can be found in reference [9]. Notethat in our case, Rn = d/2, with d being the diameter of thevane support (see Figure 2), and Rh = D/2. In the case of ahubless swirler (Rh = 0), the preceding expression reduces to

S = 2

3tan α (3)

In this study, the axial and tangential velocities U and Wwere measured at the exit of a swirling jet diffuser with a triple-probe hot wire anemometer (DISA 55M01). Four swirl numbersvalues are considered in this study. These are S = 0 for α = 0◦,S = 0.4 for α = 30◦, S = 0.7 for α = 45◦, and S = 1.3 forα = 60◦, respectively.

To carry out our experiments, the following operating con-ditions have been considered: 0 < S < 1.3, , Re0 = 30 × 103,r/D = 1 to 8, and 0 ≤ x/D ≤ 20. Here, it is useful to notethat previous studies were based on similar ranges of Reynoldsnumber (see Sislian and Cursworth [24] and Volchkov et al.[25], among others). It is worth recalling that here our goal isto identify and study the evolution of temperature profiles ofaxial and radial multijets swirling in different configurations.This approach allows analyzing the influence of key parameterssuch as angle of inclination of the vanes (α) and the numberof peripheral jets, which are controlled by a central jet. Twoconfigurations consist of three swirling jets in imbalance (A)and in balance (B) with temperature and a single swirling jetconfiguration (C) are presented in Figure 3.

NUMERICAL SIMULATION PROCEDURE

Mathematical Modeling

For a steady, three-dimensional, incompressible, and turbu-lent flow with constant fluid properties, the governing equationsof conservation of mass, momentum, and energy are written inthe Cartesian tensor notation as follows:

∂Ui

∂xi= 0 (4)

ρ∂

(UiU j

)∂x j

= −∂ P

∂xi+ ∂

∂x j

[μ

(∂Ui

∂x j+ ∂U j

∂xi

)− ρu′

i u′j

](5)

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Figure 3 Blowing configurations (T0 = 90◦C (=363 K)): (A) and (B) triple swirling jets; (C) single swirling jet.

ρC pUi∂T

∂xi= ∂

∂xi

[λ

∂T

∂xi− ρC pu′

i T′]

(6)

where U ′i and T denote the mean velocity and temperature;

u′i , u′

j and T ′ are the corresponding fluctuation components;

and −ρu′i u

′j and −ρCP u′

i T′ are the average Reynolds stresses

and turbulent heat fluxes, which need to be modeled to close theequations. It should be noted that here, the temperature varia-tions are negligible and the Mach number is low (<0.3), whichallows us to assume that the fluid is incompressible (constantdensity).

The Boussinesq hypothesis, which relates the Reynoldsstresses to the mean velocity gradients, is expressed as

−ρu′i u

′j = μt

(∂Ui

∂x j+ ∂U j

∂xi

)− 2

3

(ρk + μt

∂Ui

∂xi

)δi j (7)

where k is the turbulent kinetic energy, as defined by k = u′i u

′i/2,

and δi j is the tensor identity. An advantage of the Boussinesq

Figure 4 Schematic grid used for swirl generator.

approach is the relatively low computational cost associatedwith the computation of the turbulent viscosity μt . Note that theturbulent viscosity μt is given by

μt = Cμρk2/ε (8)

with ε being the turbulence energy dissipation rate, and Cμ is aturbulence modeling constant.

Hence in the present calculation, the turbulence scalar fluxesare modeled using the gradient-diffusion approach [26] as

ρu′i T

′ = − μt

σt

∂T

∂xi(9)

where σt = 0.6 stands for the turbulent Prandtl number.The k−ε model is an example of two equation models that use

the Boussinesq hypothesis. Here, two different closure models,the k − ε model and the Reynolds stress model (RSM), areused.

RSM Model

Two-equation turbulence models (k − ε or others) offer goodpredictions of the characteristics and physics of most flowsof industrial relevance. In flows where the turbulent transportor nonequilibrium effects are important, the eddy-viscosity as-sumption is no longer valid and results of eddy-viscosity modelsmight be inaccurate. Reynolds tress models have shown superiorpredictive performance compared to eddy-viscosity models dueto their isotropic nature. Therefore, anisotropic models such asthe full Reynolds stress transport models (RSM) are necessaryfor accurate prediction of turbulent swirling flows. In RSM, theeddy viscosity approach has been discarded and the Reynoldsstresses are directly computed.

The transport equations for the Reynolds stresses −ρu′i u

′i .

are expressed in a general form (neglecting the effects ofbuoyancy) as

∂

∂xk

(ρUku′

i u′j)

︸ ︷︷ ︸Convection

− ∂

∂xk

(μ

∂

∂xku′

i u′j

)︸ ︷︷ ︸

Molecular Di f f usion

= DT,i j︸ ︷︷ ︸T urbulent Di f f usion

+ Pi j︸︷︷︸production

+ ϕi j︸︷︷︸Pressure Strain

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Figure 5 Computational grid and boundary conditions.

+ εi j︸︷︷︸Dissipation

+ Fi j︸︷︷︸Production by System Rotation

(10)

where the various terms from left to right represent, respec-tively, convection, diffusion, production, pressure–strain redis-tribution, viscous dissipation, and additional production of thestresses. Note that the convection and production terms are ex-act, while the remaining terms have to be modeled [27]. Detailedderivations for the closure equations can be found in references[28–32], among others.

k − ε Turbulence Model

Here we briefly recall the model equations k − ε used thatclose Eqs. (4)–(7). These can be expressed as

∂

∂xi(ρUi k) = ∂

∂x j

[(μ + μt

σk

)∂k

∂x j

]+ PK − ρε (11)

∂

∂xi(ρUiε) = ∂

∂x j

[(μ + μt

σε

)∂ε

∂x j

]+ ε

k[Cε1 PK − Cε2ρε]

(12)

where Pk is the rate of production of turbulent kinetic energyand is given by

Pk = −ρu′i u

′j

∂Ui

∂x j(13)

The model constants take the following standard values [28]:σk = 1., σε = 1.3, Cμ = 0.09, Cε1 = 1.44, and Cε2 = 1.92.Note that the turbulent kinetic energy, k, is obtained directlyfrom the normal stresses.

Grid Generation

It goes without saying that the strategy of grid generationwithin the computational region and the density of the gridplay an important role in the prediction accuracy. The grid wasnonuniform, with high density in zones of great interest andlow density in zones of less interest, so that minimal compu-tational effort was required while gaining sufficient accuracy.The computational grid geometry of the swirl generator and theentire inflow system are presented in Figures 4 and 5, respec-tively. Tetrahedral mesh has been used, and in order to capturewall gradient effects, mesh has been finer toward the vanes. Inthe radial direction the mesh is fine over the test inlet and thenstretched to the exit. Tests with finer grids (up to 18 × 105 cells)demonstrate that the quality of the prediction is not improved

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Table 1 Number of cells used

Grid 1 Grid 2 Grid 3 Grid 4 Grid 5

973,556 1,797,607 1,801,362 1,801,913 1,867,537

by enhancing the number of cells used (see Table 1). Compu-tations on different mesh show that the solution of the radialdimensionless temperature in the case of configuration C doesnot change significantly (errors remain on the order of ≤4%),which suggests that the solution is independent of the mesh, ascan be seen in Figure 6.

Note that there are a total of 1,839,831, 2,244,126, and973,556 cells for blowing configurations A, B, and C, respec-tively.

Boundary Conditions

The following boundary conditions were specified in allcases simulated: at the inlet of the blowing configuration, uni-form axial velocity (6 m/s) and maximal temperature T0 =90◦C (= 363 K) and T0/2 = 45◦C (= 318 K); the initial tur-bulence intensity, I , also often referred to as turbulence level, isestimated from the following empirical correlation:

I = 0.16(ReD)−1/8 (14)

where I is given as a percentage (see Table 2), and ReD is theReynolds number based on the inner diameter D of the diffuser.

It is worth recalling that an approximate relationship betweenturbulence length scale l and the physical size of the flow diffuser

Figure 6 Sensitivity of dimensionless radial temperature variation to griddensity (k − ε model).

diameter D was used for turbulence energy modeling (see [28])

l = 0.07D (15)

Numerical Predictions

In this work, a three-dimensional numerical simulation of tur-bulent flow is presented. The Reynolds averaged Navier–Stokes(RANS) equations of the fluid flow have been solved numeri-cally using the finite volume method implemented in the FLU-ENT computer code (see [26] and [33–35]). The SIMPLE(Semi-Implicit Method for Pressure-Linked Equations) proce-dure was applied for the pressure-velocity coupling. For con-vection terms, a second-order upwind scheme has been usedto interpolate the face values of the different quantities fromthe cell-averaged values; for the viscous terms, a second-ordercentral scheme was considered. It should be noted that the facevalues of pressure terms have been evaluated using the PRESTO(PREssure STaggering Option) method. The boundary condi-tions and parameters applied for the numerical solution of theproblem are summarized in Table 2.

In the next section, we present (1) the results of the con-figuration C (single swirling jet), (2) the salient results of allconfigurations (A, B, and C), and (3) those of configurationA. For configuration C, we are interested in the effects of theinclination angle of the diffuser vanes (swirl number) on di-mensionless axial temperature and radial velocity, which areexperimentally obtained. For configurations A, B, and C, wefocus on the effect of balance and imbalance of temperature onthe dimensionless temperature profiles in the radial direction.Finally, we consider configurations A and C for presenting thedimensionless profiles of the radial temperature at several axiallocations, while quantifying the errors between experiment andprediction. Whenever it was possible, a comparison between theexperimental and numerical investigations was produced.

RESULTS AND DISCUSSION

As mentioned earlier, previous studies showed that for arange of experimental conditions, heat transfer enhancementis strongly depending on blade angle and it seems that theReynolds number has no significant influence, whereas whenthe initial vane angle of the velocity α increases, the jet is morespreading in the radial direction [15]. In this study, the dimen-sionless temperature and r− and x−coordinates were normal-ized in the forms Tr = (T − Ta) / (T0 − Ta), r/D, and x/D,respectively, where T is the jet temperature, Ta is the ambi-ent temperature, and T0 is the maximum temperature of the airblowing at origin.

Figure 7 shows the profile of the dimensionless tempera-ture in the axial direction at different velocity initial angles forthe single swirling jet (configuration C). As can be seen, theaxial temperature decreases rapidly when α increases. Hence,

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Table 2 Summary of boundary conditions parameters for the solution strategy

Parameters Configuration A Configuration B Configuration C

Turbulence intensity 7% 7% 7%Underrelaxation Pressure = 0.3, Density = 0.8

Energy = 1Other parameters = 0.6

Momentum = 0.3, Density = 0.3Other parameters = 0.5

Pressure = 0.3,Density = 1

Other parameters = 0.5Convergence criteria Energy = 10−6

Other parameters = 10−3Energy = 10−6

Other parameters = 10−3Energy = 10−6

Other parameters = 10−3

Number of cells 1,839,831 2,244,126 973,556Inlet U = 6 m.s−1, V = 0, W = 0, T0 = 90◦C (= 363 K )Pressure Presto methodwalls No-slip conditionsFree surface Pressure inletOutlet Pressure outlet

the ambient temperature is quickly reached and the area underinfluence is more important.

Figure 8 presents the comparison of our experimental andpredicted results of the radial dimensionless temperature ob-tained via the standard k − ε model for different swirler vaneangles α for the single swirling jet (configuration C). It can seenthat, only with α = 60◦, the temperature profile decreases lessrapidly, giving an important spreading compared to cases cor-responding to α = 0◦ and α = 30◦. Also, we note that the vaneangle α = 60◦ improves significantly the thermal homogeniza-tion of the flow. To this end, we chose this angle value for allconfigurations A, B, and C. It is seen from Figure 8 that thestandard k − ε model predicts the shape of the evolution temper-ature profiles in good agreement with the experimental resultsfor cases tested. However, the standard k − ε model overesti-

Figure 7 Dimensionless temperature profiles in the axial direction for differentvane angles (α = 0◦, 30◦, 60◦) for configuration C.

mates the values of the dimensionless mean radial temperaturein the region of 0.5 ≺ r/D ≺ 1.5 and underestimates thesevalues in the region of 1.5 ≺ r/D ≺ 2.3 for the case α = 60◦,which confirms the results of Wang and Mujumdar [19]. Indeed,in the swirling flows, due to anisotropy of strain and Reynoldsstresses tensors, the standard k − ε model fails to capture theturbulence effect well. The decrease in the swirl number leadsto an improvement in the quality of prediction for both cases,α = 30◦ and α = 0◦, respectively [10].

From Figures 7 and 8, we can conclude that when we in-crease the angle of the blades (α) up to 60◦, we find that theswirl number increases. Thus, the axial temperature sharply de-creases until it reaches the equilibrium temperature. In addition,the radial temperature decreases slowly and promotes a largespreading of the blown jet for good thermal homogenization.

Figure 8 Comparison of dimensionless radial temperature profiles at differentvane angles α and for x/D = 1 for configuration C.

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50 A. KHELIL ET AL.

Figure 9 Comparison of dimensionless radial main velocity profiles at vaneangles α = 30◦ and α = 60◦ for the configuration C at x/D = 1 (left side) andat x/D = 2 (right side).

These results may help to better design diffusers having vanesinclined at an angle of about 60◦. These can be used for ventila-tion applications and air conditioning to reduce harmful effectsof axial blowing on occupants and stored products.

In Figure 9, the comparison of the standard k−ε model resultsfor configuration C with the experimental data is presented.The dimensionless radial main velocity profiles at α = 60◦andα = 30◦ vane inclination and at the two locations x = 1D (leftside) and x = 2D (right side) are depicted. We note that for theangle of inclination α = 30◦, there is an absence of the centralcirculation zone and a rapid decrease in velocity compared tothe case of the angle of inclination α = 60◦. It should be notedthat the decrease of the radial velocity implies the existence ofa recirculation zone near the orifice (r close to zero). Moreover,the existence of this zone (α = 60◦) shifts the maximum of theradial velocity toward large radii. Also, examination of Figure 9shows that when the inclination angle (α) increases up to 60 ◦, theswirl number increases. Therefore, the strong swirling numberinduces a central recirculation zone that can delay jet flow. Thissuggests a large development of the blown jet, which leads to agood thermal homogenization. Moreover, we note that the modelk −ε does not reproduce correctly the experimental results. Thisresult was expected, given the nature of the model.

The comparison of measured data with numerical predictionsof the dimensionless radial main velocity profiles at α = 60◦

vane inclination for two locations x = 1D (left side) andx = 2D (right side) is highlighted in Figure 10. As solution

Figure 10 Comparison of dimensionless radial velocity profiles at the vaneangle α = 60◦ for the configuration C at x/D = 1 (left side) and x/D = 2 (rightside).

Figure 11 Comparison of dimensionless radial main velocity profiles at thevane angle α = 30◦ for the configuration C at x/D = 1 (left side) and x/D = 2(right side).

tools, standard k − ε and Reynolds stress models for turbulenceflow were used for this analysis. We note that the k − ε modelunderestimates the magnitude of the velocity at the centerline.The Reynolds stress model greatly improves the prediction ofthis quantity. Note that both models underestimate the minimumof such quantity and provide a good prediction of its maximumvalue. As can been seen, the predictions of radial dimensionlessvelocity profiles using the model Reynolds stress model are ingenerally good agreement with the experimental data.

Both models underestimate the amplitude of the velocity atthe centerline because of the inner recirculation zone, as seen inFigure 11. Outside the inner recirculation zone, the standard k−ε

and Reynolds stress models give a better overall agreement withthe experimental values. Regarding the maximum predictions,it is clear that the numerical results are much better with theReynolds stress models.

The radial temperatures profiles associated with configura-tions A, B, and C at location x/D = 8 are presented in Figure 12.

Figure 12 Radial dimensionless temperatures profiles for configurations A,B, and C at x/D = 8.

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Figure 13 Variation of the dimensionless temperature Tr vs. x/D at the center-line (r = 0) for configurations A, B, and C.

One can stress that the temperature varies slowly in the two casesof configurations A and B compared to the single jet (config-uration C). Also, the triple swirling jets with configuration Aallow a more thermal homogenization with a more importantspreading of the resulting jet compared to the B and C config-urations (see Figure 12, configuration A). Figure 13 presentsand compares the evolution of the dimensionless temperaturealong the axis of the central line for the A, B, and C configura-tions. As can be seen, the temperature approaches the ambient

temperature (Ta) beyond the station x/D = 8. The decay ismuch more visible in the case of configuration A. In this case,the stabilization occurs after the station x/D = 8. In the zone3 < x/D < 8, configuration B has a relatively stable temperaturecompared to the configuration of the single swirling jet (seeconfiguration C). Nevertheless, the general trend is quite wellmatched. For instance, the simulation using the standard k − ε

model underestimates strongly the curves for configurations Band C and overpredicts the curve of configuration A.

The radial distribution of dimensionless temperature at dis-tance from the inlets x/D = 1, 3, 5 and 8, respectively, ispresented in Figure 14. The standard k − ε and Reynolds stressmodels were used to predict the turbulence flow. Along the ra-dial coordinate, the dimensionless temperature profile movesfrom high values, decreases, and then finally approaches itsasymptotic value, which refers to ambient temperature. Somedifferences from the experimental data were observed in thezone close to the axis for x/D >3. For stations x/D = 3, 5,and 8, both models underestimate the maximum value at thecenterline. As can be seen, the temperature predictions obtainedby Reynolds stress model are generally in good agreement withour experimental data.

The radial distribution of the dimensionless temperature atdistance from inlets x/D = 1, 3, 5, and 8, respectively forconfiguration A is shown in Figure 15, which is supplementedby a figure showing the quantification of percentage errors. Inthis addendum, E-RSM and E-k-ε denote the percentage of er-rors with the models RSM and k − ε, respectively. Recall thatconfiguration A consists of a central hot flow blown in the op-posite sense of rotation of adjacent fluxes that are less heatedthan the central flux. Among all the studied configurations, con-figuration A ensures maximum temperature stability in the ra-dial direction with a fast homogenization compared with other

Figure 14 Radial distribution of the dimensionless temperature Tr at x/D = 1, 3, 5, and 8 for configuration C.

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Figure 15 Radial distribution of the dimensionless temperature Tr at x/D = 1, 3, 5, and 8 with quantification of errors (configuration A).

configurations. The stability starts at station x/D = 5 with a0.2 amplitude for this configuration as shown in Figure 15, andat station x/D = 8 with a 0.5 magnitude for configuration Cas shown in Figure 13. Returning to Figure 15, we note thatalong the radial coordinate, the dimensionless temperature pro-files have two peaks characterizing the mixing zone. Then they

gradually decrease to the asymptotic value that is the ambienttemperature. Overall, the predicted results are in good agree-ment with experimental data but there is a small discrepancy inprediction of the radial development of stability zone. Outsidethis zone, we note that Reynolds stress model significantly im-proves the results. Moreover, the quantification of errors shows

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Figure 16 Radial distribution of the dimensionless turbulent energy (k∗ = k/U 20 ) at locations x/D = 5, 6, 7, and 8.

that the RSM model clearly minimizes errors.In Figures 16 and 17, the radial profiles of dimensionless

kinetic turbulence energy (k∗ = k/U 20 ) and dissipation rate en-

ergy (ε∗ = εD/U 30 ) are plotted at different axial locations. These

profiles are presented here to provide a qualitative idea of theturbulence generation processes in the shear layers of the jets.In the case of a single swirling jet (configuration C), we ob-serve one peak near the orifice, and then two peaks far from theorifice corresponding to the location of the shear layer, therebyconfirming that homogenization has not yet occurred. For theconfiguration of triple swirling jets (A and B), the dimension-less profiles of turbulence kinetic energy and its dissipation rateexhibit two distinct peaks at small axial distance x/D. We con-jecture that these two peaks indicate approximately the locations

of the shear layer for the central jet and peripheral jet, respec-tively. After mixing of the peripheral and central jets, a singlepeak remains. This peak gradually moves from the shear layerregion toward the axis of the fully developed jet, thus leadingto thermal homogenization. Due to its asymmetry in terms oftemperature, configuration A has high turbulence intensity at agiven station. This finding confirms the fact that in regions nearthe diffusers, the turbulent kinetic energy is higher for the mul-tiple jets than for the swirling single jet. This is conspicuous inFigures 16 and 17, where k∗ and ε∗ decrease sharply in cases Aand B, compared to the single swirling jet case. It is interestingto note that the simulation achieves easily some quantities suchas the energy-dissipation rate, which is notoriously difficult tomeasure experimentally in laboratory jet flows at small scales

Figure 17 Radial distribution of the dimensionless dissipation rate (ε∗ = εD/U 30 ) at locations x/D = 5, 6, 7, and 8.

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Figure 18 Comparison of temperature contours for configurations A, B, and C at the plane y = 0.

compared to that of the mean motion. Indeed, special attentionshould be paid to the effects of spatial resolution on the estima-tion of such a quantity. For further details, the interested readercan turn to the abundant literature about this topic.

Figure 18 shows contour plots of the temperature for con-figurations A, B, and C. Note that this figure is composed oftwo parts: The top part is a three-dimensional illustration ofjets, while the bottom part is the temperature mapping in theplane (x, z) at the plane y = 0. Through this mapping, we seethat thermal homogenization occurs rather sharply in the caseof configuration A because of rapid thermal stabilization.

CONCLUSIONS

In this work, an experimental and numerical study of differentconfigurations of blowing multiple swirling jets for use in venti-lation applications has been fulfilled. The numerical simulationof the flow and temperature fields has been carried out usingthe standard k − ε and the Reynolds stress turbulence models.Based on the investigation conducted for different configura-tions and parameters, the following conclusions can be made.We have highlighted more improvement of the thermal homog-enization of the treated area using multiple swirling jets with anappropriate choice of the position for blowing air. The analy-sis of the flow features clearly demonstrates that the interactionbetween swirling jets induces the redistribution of temperaturein the mixing zone, while allowing the spreading of the result-ing jet. It appears that the central jet plays an important rolein the enhancement of the thermal homogenization. From thethermal homogenization viewpoint, with the parametric studyof the diffuser geometry, the swirler vane angle, the numberof blowing jets, and the direction of rotation, balance and im-

balance in temperature between the central and peripheral jetsare adequate means to enhance the quality of thermal homoge-nization. Thus, when the vanes inclination increases, the axialvelocity decreases and the jet spreads radially. Under these con-ditions, along the flow, the axial temperature decreases and theradial temperature increases. When comparing the evolution ofthe axial and radial temperature, configuration A shows a bet-ter radial stability with an axial decay importance. Of all theconfigurations studied, configuration A insures maximum andfaster radial temperature stability. Overall, obtained quantitieswith the Reynolds stress model are in better agreement withthe experimental data compared to those of the standard k − ε

model.

ACKNOWLEDGMENTS

Fruitful discussions with Gary Manner (University of Artois,France) are gratefully acknowledged. We are also indebted tothe editor in chief and anonymous referees for their insight-ful comments and suggestions that improved the quality of thepresent work.

NOMENCLATURE

CP heat capacity, J/kg-KCμ, Cε1, Cε2 turbulence model constantsd vane support diameter, mD inner diameter of one diffuser, me spacing between diffusers, mE − k − ε errors’ percentage with the k − ε modelE − RSM errors’ percentage with the RSM modelGθ axial flux of tangential momentum

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Gx axial momentum fluxI initial turbulence intensity (= 100[(u′2 + v′2+

w′2)/3]1/2/U ) defined in Eq. (14)k turbulent kinetic energy, m2/s2

k∗ dimensionless turbulent kinetic energy(= k/U 20

)l turbulence length scale, m•m mass flow rate, kg/sP pressure, PaPk rate of production of turbulent kinetic energy,

kg/ms3

Re0 Reynolds number at air blowing origin, dimen-sionless

ReD the Reynolds number based on the inner diame-ter D, dimensionless

r radial coordinate of air flow, mR characteristic radius, mRh radius of the inlet duct, mRn radius of the centre body, mS swirl number, dimensionlessT temperature of jet, KTa ambient temperature, KT0 maximum temperature of the air blowing at ori-

gin, KTr dimensionless temperature

(= (T − Ta)/ (T0 − Ta))u′ fluctuating velocity, m/sρu′

i u′j Reynolds stresses, kg/ms2

Ui velocity components, m/sU0 maximum value of the velocity of the air blowing

at origin, m/sU mean axial velocity based on flow rate, m/sW mean tangential velocity, m/sx axial coordinate of the air flow, m

Greek Symbols

α inclination angle of the vanesε turbulence energy dissipation rate, m2/s3

ε∗ dimensionless dissipation rate(= εD

/U 3

0

)λ thermal conductivity, W/m.Kμ dynamic viscosity, kg/msμt turbulent viscosity, kg/msρ air density, kg/m3

σk, σε turbulent Prandtl numbers, dimensionless

Subscripts

i, j component indicest turbulentθ tangential direction

x axial direction

Superscripts

− time average∗ dimensionless quantity

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Ali Khelil received his diploma in mechanical en-gineering from Chlef University (Algeria). In 2001,he obtained a magister in mechanical engineering. In2006, he joined Lille 1’s University of Sciences andTechnologies, Polytech’Lille, to pursue the degree ofdoctor in mechanical engineering. He obtained hisdegree of doctor in 2008. Since 2008, he has been anassociate professor at University of Chlef, Algeria.His research activities are on combustion (numeri-cally and empirically), computational fluid dynamics,

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and heat transfer. Since 2001, he has participated in several national and inter-national meetings and scientific conferences. He is author and co-author of over20 referred journal papers.

Hassane Naji is a full professor of mechanical engi-neering at Artois University (France). He received hisundergraduate and graduate education in the Mechan-ical Engineering Department of Lille 1 University(France). Following research engineer and assistantprofessor positions at Rouen University and INSA,Rouen, France, he joined Polytech’Lille School ofMechanical Engineering–Lille 1 University as an as-sociate professor until 2010, and then moved to theArtois University (AU). He holds a Ph.D. in physical

sciences from the University of Lille 1 (France) and an M.Sc. in thermal-fluidsciences from the National Polytechnic Institute of Lorraine (INPL), Nancy,France. His research and teaching focuses on thermal-fluid sciences and engi-neering, advanced heat transfer, numerical methods for multiscale simulations(mesoscopic and macroscopic approaches), and applied thermodynamics forengineering. In terms of research, he is the author of more than 100 referredarticles in international journals and conferences. Also, he is a referee for manyscientific journals.

Mohamed Braikia obtained a magister in mechani-cal engineering from Oran University (Algeria). Cur-rently, he is an associate professor at the Universityof Chlef, Algeria, since 2002, and he is involved inseveral projects regarding turbulence and heat trans-fer. His research works and teaching concern experi-mental techniques, numerical and experimental ther-moflow, computational fluid dynamics, and thermal-fluid sciences. Since 2001, he has participatedin several national and international meetings and

scientific conferences.

Larbi Loukarfi is a full professor at Chlef Univer-sity (Algeria) since 2004. He has been Vice-Presidentof Research at Chlef University, and he is involvedin several projects regarding turbulence, heat andmass transfer, and renewable energy. Since 1998,he has participated in several national and interna-tional meetings and scientific conferences. His re-search studies and teaching subjects include thermal-fluid science and engineering, fundamentals of ad-vanced energy conversion and combustion, advanced

fluid mechanics, and turbulence. He is author and co-author of more than 40referred journal papers.

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