Experiment and Large-Eddy Simulation on Free Air Jets Issuing from a Rectangular Nozzle with Deflectors

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Introduction
Having a good understanding of vortical structures in free shear layers such as jets is important for the control of aerodynamic noise and the enhancement or suppression of flow mixing.Methods of enhancing and suppressing mixing in jet flows have been studied for the past half-century.Numerous studies on jets issuing from a non-circular nozzle have been conducted [1]- [11].Particularly, triangular [3], square [4], rectangular [5] [6], and elliptical [7] jets can improve the mixing performance in the flow field.
Rectangular jets essentially combine the effects of the aspect ratio observed in elliptic jets and the corners observed in square jets.The flow structure in the rectangular jet contains streamwise vortices produced by secondary flow at the corner of the nozzle.The deformation of the rectangular vortex ring persists downstream and plays an important role in the spreading of this type of jet.Sfier [5] examined jets issuing from rectangular slots with different geometries and aspect ratios.It was found that the nozzle geometry plays a very important role in determining the rectangular jet development through the three-dimensional effects of the flow, and, in comparison to orifice jets, the flow emitted from the rectangular channel has a two-dimensional region that extends further downstream.Quinn [6] studied the influence of the aspect ratio on the turbulent free jet flow issuing from sharp-edged rectangular slots.His results demonstrate that the near-field mixing in the rectangular jet increases with increasing slot aspect ratio.In the case of an aspect ratio of 20, the jet had the shortest potential core and the highest shear-layer values of the turbulence kinetic energy and the Reynolds stress.
The effects on a jet of notches, grooves, tabs, and deflectors placed in the near nozzle exit have also been studied.Fujita et al. [8] measured the potential core length, velocity decay, and half-velocity width of a 12.5:1 rectangular jet with rectangular notches.It was revealed that the potential core length takes a maximum value in the case of a notch aspect ratio of 12.5, causing a large secondary flow toward the jet centerline in the upstream region.Kumar et al. [9] conducted experiments on jets from a 2:1 rectangular nozzle with and without grooves.
They demonstrated that the grooves do not significantly influence the overall jet mixing characteristics but considerably influence the axis-switching phenomenon.Verma et al. [10] experimentally studied a jet issuing from an elliptic nozzle with two cylindrical tabs at a Reynolds number of 5.08 × 10 4 .Increasing the tab height shifted the location of the end of the jet potential core further upstream and promoted higher jet half-width growth along the plane of the major axis.As a result, axis switching in the tabbed elliptic jet was not observed.Hinomoto et al. [11] examined the effect of deflectors installed symmetrically inside an 8.8:1 rectangular nozzle on the flow characteristics of the elongated rectangular jet with the side walls.It was found that the spread of a plane jet with divergent deflectors is larger than that of a jet with no deflectors.However, the spread of a plane jet with convergent deflectors is smaller than those of jets with divergent deflectors and without deflectors.However, it is unknown that the deflectors inside the rectangular nozzle with a low aspect ratio are effective to control the spread of a rectangular jet which has the three-dimensional flow structures such as the axis-switching phenomenon.Thus, the purpose of this study is to establish eventually a passive flow control method for the spread of a rectangular jet with AR = 2.17 using deflectors installed symmetrically inside a nozzle.This aspect ratio was determined by referring to the dimensions of the nozzle of a car air conditioner.The present paper was investigated using two-component hot-wire anemometer measurements and three-dimensional numerical simulation by the large-eddy simulation (LES).
Our final goal is to make the small spread rectangular jet.

Experimental Setup
Figure 1 shows a schematic diagram of the experimental apparatus.Velocity measurement and flow visualization were carried out using a blow-down wind tunnel.An axial fan was used to supply airflow to the rectangular nozzle.The rectangular nozzle had a double contraction with dimension reduction ratios of 3.3:1 and 2.8:1.Figure 2 shows three-dimensional diagrams and cross-sections of rectangular nozzles with parallel plates and deflectors.The rectangular nozzle had a height H of 30 mm, a width B of 65 mm, and a length of 100 mm.The thickness of the deflector plate t was 0.8 mm.The angles between the parallel plates, the divergent deflector plates, and the convergent deflector plates were α=  0˚, 6˚, and −6˚, respectively.The mean and fluctuating velocities were measured using an X-type hot-wire probe and a constant-temperature hot-wire anemometer with a linearized output.The output signals of the hot-wire probe were converted by a 12-bit analog-to-digital (A/D) converter with a sampling frequency of 10 kHz, and 10 5 data points were stored.A computer-controlled traversing mechanism was used for probe positioning.Experiments were performed under computer control for automated data acquisition.The mean velocity and turbulence intensity were obtained using a personal computer.The velocity profile for the rectangular jet at the nozzle exit exhibited a flat-topped shape.The mean bulk velocity U 0 and the turbulence intensity 0 rms u U ′ at x/H = 0.1 from the nozzle exit were 4.5 m/s and 0.7%, respectively.This wind speed corresponds to the low level of a car air conditioner.The Reynolds number Re H (=U 0 H/ν, where ν is the kinematic viscosity of air) was approximately 9000.
Flow visualization was carried out under the same conditions as the flow measurement experiments.To visualize the flow, an oil mist was injected into the wind tunnel.A pulsed Nd:YAG laser was used to visualize vortical structures, and images were recorded by a CCD camera.

Computational Techniques
Three-dimensional numerical simulations were performed using the large-eddy

Mean Velocity and Turbulence Intensity in the x-y and x-z Cross Sections
Figure 4(a) shows the profiles of the mean streamwise velocity ū/U 0 in the x-y plane along the minor axis at z = 0, and the x-z plane along the major axis side at y = 0 to compare the four jets, i.e., nozzles with no deflectors, parallel plates, divergent deflectors, or convergent deflectors.The streamwise velocities were normalized with respect to the mean bulk velocity U 0 .With respect to the velocity distribution at x/H = 0.1 separated by deflectors, the jet on the central axis side is referred to as the inner jet, and the jets on both sides of the inner jet are referred to as the outer jets.The velocity profiles of the jets show good symmetry, in contrast with the central axis.For the jet with parallel plates, a velocity depression occurs between the inner and outer jets due to the wake of the parallel plates at x/H = 0.1.However, the ratio of the maximum velocity of the inner jet ū imax to the outer jets ū omax is ū imax /ū omax = 1.0, namely, each maximum velocity is approximately the same, since the angle between the parallel plates is 0˚.For the jet with divergent deflectors, the velocity profile at x/H = 0.1 exhibits a concave shape, and the velocity ratio is ū imax /ū omax = 0.8.Further downstream at x/H = 6, the concave shape disappears as the jet takes on a fully developed profile.In addition, the jet spread is larger than that of the other three jets.For the jet with convergent deflectors, the velocity ratio is ū imax /ū omax = 1.3.The velocity profile has a convex shape at x/H = 0.1, that is, the velocity of the inner jet is larger than that of the outer jets.The jet spread at x/H ≥ 3 is smaller than that of the other three jets.It can be seen that velocity profiles similar to that of a coaxial jet [12] are obtained by installing deflectors inside the rectangular nozzle.Some interesting features can be observed in the x-z plane.The jet spread for divergent deflectors is the smallest for these three jets at x/H = 6.In contrast, the jet spread for convergent deflectors is the largest for these three jets.These result in the direction opposite the mean streamwise velocity in the x-y plane.Figures 4(b)-(d) show the profiles of mean streamwise velocity ū/U 0 in the x-y and x-z cross sections for the three jets in order to compare the experimental results and the results of the numerical simulation.The experimental and numerical LES results show good agreement in the region from the nozzle exit at x/H = 0.1 to the jet downstream region at x/H = 6.These results demonstrate that the LES simulation can reproduce the actual flow field. of the fluctuating streamwise velocity components in the x-y plane along the minor axis at z = 0, and the x-z plane along the major axis side at y = 0 to compare the three jets.In the x-y plane, the velocity fluctuation for the jet with divergent deflectors near the center of the nozzle at x/H = 0.1 is larger than that for the jet with convergent deflectors as a result of flow separation on the inner nozzle wall.At x/H = 6, the velocity fluctuation for the jet with divergent deflectors at the outer side of jet is larger than that for the jet with convergent deflectors.This phenomenon is related to the larger amount of spreading near the nozzle exit for the jet with divergent deflectors.For the jet with convergent deflectors, the velocity fluctuation near the centerline is smaller than those for the other jets.However, the turbulence intensity near the centerline at x/H ≥ 5 increases more than that for the jet with divergent deflectors.In addition, for the x-z cross section, the velocity fluctuation at the nozzle exit is larger than that for the jet with convergent deflectors, and the growth rate for the velocity fluctuation near the centerline is low.

Mean Velocity and Turbulence Intensity along the Jet Centerline
Figure 6 shows the mean streamwise velocity along the jet centerline in the experiment.The local centerline velocity ū is normalized by the bulk velocity U 0 at the nozzle exit.The potential core length x p , which is defined as the distance between the nozzle exit and the point at which the centerline velocity has decayed to 95% of its maximum value [13], is approximately 7H, 8H, 0.5H, and 10H for the jets with no deflectors, parallel plates (ū imax /ū omax = 1.0), divergent deflectors (ū imax /ū omax = 0.8), and convergent deflectors (ū imax /ū omax = 1.3), respectively.In short, the length of the potential core also increases as the velocity ratio increases.This result agrees with previous experimental studies performed by Warda et al. [14] [15] and Mergheni et al. [16].For divergent deflectors, the centerline velocity ū c /U 0 decreases from the vicinity of the nozzle exit and then Figure 6.Profiles of mean streamwise velocity ū c /U 0 on the jet centerline.
has a minimum value at x/H = 3.This is similar to the results of Durao and Whitelaw [17] and Buresti et al. [18] whereby the velocity decay ratio of the centerline velocity ū c /U 0 decreases immediately after the jet issues from the nozzle exit and the potential core length becomes short.In the far field at x/H > 10, the centerline velocity decreases at ū c /U 0 ~ x −1 for all four jets, that is, this velocity decay ratio demonstrates behavior similar to that of a fully developed circular jet.Thus, this result shows that the rectangular jets with and without deflectors ultimately evolve into fully developed circular jets.
Figure 7 shows the RMS value for the streamwise velocity fluctuations along the jet centerline in the experiment.For the jet with divergent deflectors, the velocity fluctuation at x/H < 3 in the near field is larger than that for the other jets.However, the velocity fluctuation at x/H > 5 is small in comparison with that for the other three jets.In the far field at x/H > 20, there is little difference between the velocity fluctuations for the four jets.

Growth of Jet Half-Velocity Width
Figure 8 shows the growth of the jet half-velocity width obtained experimentally in the x-y and x-z planes.For the jet with no deflectors, the jet spreads rapidly along the minor axis in the x-y plane and more slowly along the major axis in the x-z plane.The axis-switching location x as /H, where the length of y 1/2 /H and z 1/2 /H is reversed as a result of axis switching, is at x as /H ≈ 16 (Figure 8(a)).In the case of the jet with parallel plates, axis switching occurs closer upstream (x as /H ≈ 8) than the jet with no deflectors because the value of z 1/2 /H does not change much for x/H < 8 (Figure 8(b)).The jet with divergent deflectors spreads rapidly along the minor axis in the x-y plane and shrinks along the major axis in the x-z plane.As shown in Figure 8(c), the value of z 1/2 /H shows a decrease in the range of x/H from 0 to around 8 in x increases because of the relative low velocity area near the jet centerline, i.e. the ratio of the maximum velocity of the inner jet ū imax to the outer jets ū omax is ū imax /ū omax = 0.8.As a result, the jet shrinks the z-direction.Axis switching also occurs closer to the nozzle exit (x as /H ≈ 4)  Therefore, the deflectors installed inside the rectangular nozzle influence the axis-switching location of the rectangular jet.

Equivalent Jet Half-Velocity Width Growth
Figure 9 shows the equivalent jet spread, i.e., the equivalent jet half-velocity width (y 1/2 × z 1/2 ) 0.5 /H [19], along the x-axis non-dimensionalized by the height of the nozzle.For comparison, the figure also reports the data of Kumar et al. [9] for a rectangular jet with an aspect ratio of 2 and Quinn [20] for a planar jet with an aspect ratio of 20.The equivalent jet spread signifies the overall spread of the jet along the x-axis based on the given exit conditions.The equivalent jet spread for the nozzle with no deflectors is greater than that for the nozzle with divergent deflectors and less than that for the nozzle with the convergent deflectors.
The jet spread along the minor axis is made dominant by the introduction of deflectors inside the nozzle.Although the jet half-velocity widths y 1/2 /H and z 1/2 /H in each plane shown in Figure 8 exhibit nonlinear variation with x/H, the equivalent jet half-velocity width (y 1/2 × z 1/2 ) 0.   of Kumar et al. [9] and Quinn [20].Therefore, the jet spread data in Figure 9 were fitted by linear regression analysis using the function ( ) where K s is the spreading rate, and C s is the geometric virtual origin.The values of these parameters obtained in the fitting are given in Table 1 for each of the cases plotted in Figure 9.There is a difference between the spreading rates K s for the 2.17:1 and 20:1 rectangular jets.In general, rectangular jets with small aspect ratios generate three-dimensional flow fields, whereas those with large aspect ratios generate two-dimensional flow fields.Note that the spreading rate K s for the jet with divergent deflectors is larger than those for the other jets.

Deformation of Jet Outline
Figure 10 shows the contours of mean streamwise velocity for the three jets obtained experimentally in the quarters of the y-z plane at x/H = 1, 4, 10, and 16.These measurements of grid points were carried out for a step size of Δy = Δz = 1.0 mm for x/H = 1, Δy = Δz = 2.0 mm for x/H = 4, and Δy = Δz = 5.0 mm for x/H = 10 and 16, respectively.The contour interval is 0.1U 0 .As shown in Figure 10(a), immediately downstream of the nozzle exit, i.e., x/H = 1, the rectangular jet with no deflectors retains the original shape of the rectangular nozzle, and the jet has a thin shear layer at the circumference of the nozzle.The jet deformation begins at the nozzle corners because of the nonuniform velocity induction (seen as an outward bump in the contours).As a result, the ambient fluid was brought in toward the jet centerline along the major axis side while the jet fluid was ejected along the minor axis side.Further downstream, the shear layer becomes thick and the shape of the jet changed as there was high growth along the minor axis side.The outline of the jet at x/H = 16 changes from rectangular to diamond-shaped, accompanied by axis switching.In the case of the jet with parallel plates (Figure 10(b)), the velocity defect occurs due to the wakes of the parallel plates at x/H = 1.However, the jet maintains a rectangular shape, as is the case for a jet with no deflectors.The axis switching occurred for x/H > 10.In the Journal of Flow Control, Measurement & Visualization case of the jet with divergent deflectors (Figure 10(c)), at x/H = 1, the velocity in the outer mixing region is larger than that in the inner mixing region.The thickness of the shear layer at the long side of the rectangular nozzle at x/H = 4 is thinner than that at the short side.The jet outline is extended by high growth along the minor axis side for x/H > 4. As a result, the jet shape changes from a lateral rectangle to a vertical ellipse.On the other hand, as shown in Figure 10(d), the jet with convergent deflectors has a thin shear layer at the short side of the rectangular nozzle at x/H = 1, as compared with the long side.The jet extends more rapidly along the major axis side than along the minor axis side.
Consequently, the jet outline at x/H = 16 roughly maintains the rectangular shape of the nozzle exit without axis switching occurring.The flow structures can be changed by adjusting the deflectors.These results are consistent with the instantaneous flow visualization images qualitatively, as shown in Figure 12.For the jet with no deflectors, the periodic vortical structure, i.e., the vortex ring in the x-y cross section is arranged symmetrically with respect to the x-axis and changes to a small-scale vortical structure in the downstream.On the other hand, for the jets with divergent and convergent deflectors, the large-scale vortical structures are not clear in the shear layers.

Instantaneous Vorticity Contours and Vortex Shedding Frequency
Figure 13 shows the power spectra of the streamwise fluctuating velocity in the outer (x/H = 0.5, y/H = 0.5, z/H = 0) and inner (x/H = 0.22, y/H = 0.22, z/H = 0) mixing regions obtained by the numerical simulation.For the jet with no   These vortical structures agree with the instantaneous images of rectangular jets in the x-y plane qualitatively, as shown in Figure 12.

Conclusions
The influence of the angle between two plates inside the nozzle, i.e. divergent and convergent deflectors, on the flow characteristics and vortical structures of a rectangular jet with an aspect ratio of AR = 2.17 was investigated experimentally and through large-eddy simulation.The following conclusions were reached in the present study.
1) The mean velocity distributions obtained by numerical simulations using LES are in good agreement with the experimental results.The turbulence intensity distribution obtained by LES is in approximate agreement with the experimental results.LES can accurately simulate the three-dimensional flow structures of rectangular jets with deflectors.
2) In the case of the jet with divergent deflectors, a small-scale vortical structure is generated in the outer shear layer, and the turbulence intensity in the inner mixing region is high because of the separated flow on the deflector walls.As

Figure 1 .
Figure 1.Schematic of the experimental apparatus.

Figure 2 .
Figure 2. Schematic diagram of the rectangular nozzle with deflectors and the cross-section of nozzles.(a) Parallel plates; (b) Divergent deflectors; (c) Convergent deflectors.

Figure 3 .
scheme was used for the time marching.The computational domain, mesh, and boundary conditions are shown in Figure3.The streamwise and transverse lengths of the computational domain were set to 600 mm (=20H) and 450 mm (=15H), respectively.The nozzle geometry was defined to correspond to the experimental setup (H = 30 mm, B = 65 mm).Since the boundary layer in the deflectors occurs the flow separation on the walls easily and turbulence models must be quite sensitive in the vicinity of the mesh spacing near the wall and nozzle to yield accurate predictions, the computational meshes used for the LES were set finer than those for the laminar simulations.Therefore, the minimum cell size is 0.1 mm near the walls.The numbers of grid point in the x, y, and z directions were 231, 222, and 251, respectively.A total of approximately 1.1 × 10 7 grid points were nonuniformly distributed in the computational domain.The Courant number is less than 0.1.A uniform velocity profile corresponding to the nozzle exit velocity was specified at the inlet boundary.The velocity on the upper and lower inlet surfaces, which were outside of the rectangular nozzle inlet surface, was adjusted to 0.03U 0 to maintain a weak straight flow aligned toward the entrainment flow outlet[12].The nonslip boundary condition was applied to the walls of the rectangular nozzle.The slip condition was applied at the periphery of the computational domain, where the gradients of all variables were set to be equal to zero.A pressure outlet condition of p = 0 was specified at the downstream boundary of the domain.

Figure 5 (
Figure 5(a) shows the profiles of the root mean square (RMS) values 0 rms u U ′
Figures 5(b)-(d) show the profiles of the RMS values 0 rms u U ′ for the fluctuating streamwise velocity components in the x-y and x-z cross sections for each jet to compare the experimental results and the results of the numerical simulation.For the jet with no deflectors, the LES results show fair agreement with the experimental results from near the nozzle exit at x/H = 0.1 to downstream at x/H = 6.On the other hand, the agreement between the experimental and numerical results for the jets with divergent and convergent deflectors is poor in the upstream region.This difference may be caused that the transition flow from the flow of the relative low Reynolds number (Re = 9000) to the turbulent flow cannot simulate with accuracy by the LES.

Figure 7 .
Figure 7. Profiles of the RMS streamwise velocity fluctuation 0 rms u U ′ on the jet cen-

Figure 8 .
Figure 8. Variations in the jet half-velocity width in the x-y and x-z planes.(a) No deflectors; (b) Parallel plates; (c) Divergent deflectors; (d) Convergent deflectors.
5 /H varies linearly with x for x/H > 10.The spreading rate for the present jets shows close agreement with the data Journal of Flow Control, Measurement & Visualization

Figure 11 Figure 11 .
Figure 11 shows instantaneous vorticity contours in the x-y plane along the minor axis side at z = 0 for the three jets obtained by the large-eddy simulation.Vortex roll-up is observed in the shear layers at the nozzle exit, and vortices of opposite signs are positioned symmetrically about the jet centerline at x/H ≈ 1.2 for the jet with no deflectors (as shown in Figure 11(a)).For the case of the jet

Figure 14 shows
Figure14shows instantaneous three-dimensional vortical structures for the three jets based on the second invariant isosurfaces of the velocity gradient tensor Q.In the case of the jet with no deflectors (Figure14(a)), the vortex rings are generated and maintained periodically from the nozzle exit until x/H ≈ 3.The vortex ring collapses, and vortical structures, such as hairpin vortices, are

Figure 14 .
Figure 14.Second invariant isosurface of the velocity gradient tensor Q for the rectangular jets.(a) No deflectors; (b) Divergent deflectors; (c) Convergent deflectors.

Table 1 .
Spreading rates and geometric vertical origins obtained by fitting experimental data with Equation (1).