Numerical and Experimental Investigation of Near-Field Mixing in Parallel Dual Round Jets

Parallel underexpanded round jets system has been widely used in engineering applications, and the flow field structures are very complex because of the jets interaction. In this paper, we studied the near-fieldmixing phenomenon in parallel dual underexpanded jets numerically by solving the Reynolds-Averaged Navier-Stokes Equations. The numerical results agree well with experimental data acquired by particle image velocimetry. Similar to plane jets, to some degree, two round jets are deflected towards the dual nozzle symmetry plane; the flow field can also be divided into three regions. Meanwhile, attempts have been made to predict merge point and combine point locations on certain cross profile of computational domain by correlating them with jet spacing and jet pressure ratio.The jet spacing plays an important role in jets interaction, and jet interaction decreaseswith the increase in jet spacing. The jets interaction in terms of merge (combine) point and pressure varies significantly while the jet spacing differs. Additionally, as pressure ratio increases, the effect of jet interaction decreases, and the merge (combine) point location moves downstream.


Introduction
Parallel jets issuing from adjacent nozzles into still surroundings gradually merge into a single jet at a certain distance downstream, which has been widely used in many engineering applications such as vertical take-off and landing of airplanes, fuel-injection systems, and supply devices in ventilation systems [1,2].In fact, there has been significant research effort dedicated to the coupling relationship of the jets [3][4][5][6].However, coupling relationships of the jets are not fully understood yet.The previous reports reveal that three relevant regions of the flow field in axial direction were identified for the two-plane parallel jets [7][8][9].Figure 1 shows the general flow field of two-plane parallel jets.The first region is converging region from nozzle exit to the point where the inner shear layers of the jets merge (termed as the merge point).At the merge point the velocity in the jet flow direction on the symmetry plane is zero and the pressure reaches the highest value [10,11].The location where the velocity at the symmetry plane reaches its maximum is called the combined point and denotes that the merging region ends and the combined region begins [12,13].The combined region is downstream of the combined point where the two jets begin to resemble a self-similar single jet [6,[14][15][16].
However, for the round nozzles, the three-dimensional flow structures need to be taken into consideration, and jets will interact and the position of maximum velocity will shift from the symmetry axis to the symmetry plane between the nozzles [17].Numerical simulations of two round jets by Allen and Smith [18] indicated that the results of the standard - model are consistent with experimental data for parallel jets with low inlets.Harima et al. [3,19] showed that the widely used turbulence models (RNG - model and realizable - model) can be used to predict mean velocity and turbulence properties in the near zone of interacting confluent round jets with low inlets precisely.
Wang [20] researched on the based flow for four-engine clustered nozzle, where a standard two-equation turbulence model was used to describe the turbulence, and a pressure inlet condition was imposed on nozzle inlet plane.The numerical results coincided well with the experimental results.
Although confluent jet phenomenon has been a topic of great interest to researchers over the past decade, there  remain few literatures on prediction for the critical mixing regions (such as the merge point and the combine point) of parallel dual underexpanded jets.Furthermore, experimental investigations on the confluence of parallel dual underexpanded jets are sparse.This study is focused on near-field mixing phenomenon of dual underexpanded jets, and the PIV measurement and numerical simulation are used to study the jet interaction and its resulting characteristics.The main objectives are to gain insights into the complex phenomena occurring in this near-zone region and to obtain accurate and detailed experimental data that can be used to verify the numerical results.The PIV measurement and numerical simulation are used to study the jet interaction and its resulting characteristics.Furthermore, the effect of jet-to-jet spacing (/  ) and the jet pressure ratio have been investigated.The jet pressure ratio has value of total pressure  0 in the settling chamber divided by back pressure   . 0 /  are 3.4, 6.8, and 8.1 in this study, respectively.

Experimental Procedures
Table 1 shows all the tests conducted in the experimental setup.High pressure gas at ambient temperature (300 K) is discharged into enclosure through a pair of converging circular nozzles.According to the jet pressure ratio, we divided the tests into three groups by using eight converging circular nozzles plates.3. The CCD camera is mounted perpendicularly to the light sheet.The raw images were postprocessed with the commercial software DaVis 7.2.2.The seeding density is high enough to assume an order of magnitude displacement uncertainty of 0.1 pixels [21], which yields an uncertainty in the velocity field between 1% for the high velocity region and 20% for the low velocity regions.According to the practical guidelines by Adrian and Westerweel [22], the uncertainty of the instantaneous velocity field is estimated within ±3%.The maximum statistical error, due to the finite number of samples (with 95% confidence), is less than ±1.4% for mean velocities and less than ±0.8% and ±0.3% for normal and shear Reynolds stresses.used on the walls parallel to the flow direction; and the pressure inlet boundary condition is applied to the nozzle inlet..Reynolds-Averaged Navier-Stokes Equations for three-dimensional compressible flows are given by

Governing Equation
where the overbar indicates a time-averaged variable.

The RNG 𝑘-𝜀 Model.
In this study, we employ the RNG - model for high Reynolds number flow given by Yakhot et al. [23]: with 3.4.Numerical Scheme.The above transport equations have been solved using the standard FLUENT software in version 13.0 by Finite Volume Method.The implicit formulation and Roe-FDS flux type are for density-based solver type.The Green-Gauss Cell Based scheme is used for gradient discretization.Second-order upwind central differencing is used for flow terms, while first-order upwind central differencing is used for turbulent kinetic energy and turbulent dissipation rate.The solutions are considered to be converged when absolute values of the residuals are below 1 × 10 −5 .The standard wall functions are used in the near-wall modeling.
3.5.Wall Yplus and Mesh Independency Tests. Figure 5 illustrates the computational mesh which consists of mesh, consists of structured hexahedral cells, and is refined closely to the wall, due to the high velocity gradients in this region.In order to eliminate grid quantity and quality effects on  the numerical results, wall Yplus and mesh independency tests must be done using different mesh densities and grid configurations.Here, the mesh model (/  = 2,  0 /  = 6.8) was taken as an example to illustrate the wall Yplus and        Figures 6 and 7 show the predictions of velocity and pressure at the line  = 0 (on the plane  = 0) along the flow field downstream, respectively.And the results are obtained on the three different mesh sizes, namely, 1.28 million, 2.83 million, and 4.11 million.The results difference between predictions of 1.28 million meshes and 2.83 million meshes is higher than the difference between 2.83 million meshes and 4.11 million meshes.It is indicated that the mesh size will slightly affect the numerical result when it is larger than 2.83 million.Therefore, the model with 2.83 million meshes' size is chosen to improve computing efficiency.

Results and Discussions
4.1.Characteristics of Double Jets.The characteristics profiles of mean velocity along the downstream location are presented in Figure 8. From Figure 8(a), we find that the double jets on both sides lean and bend towards the central symmetrical plane.Along the downstream location, the double jets gradually resemble a self-similar signal jet. Figure 8 demonstrates the velocity from numerical results at different downstream cross sections up to /  = 80. Figure 8 shows several features of the development of confluent jets.The faster merging of jets can be clearly observed; for example, /  = 28.At the nozzle exit, high velocities lead to entrainment of gas in the shear layers of the jets.Entrainment rates in the region between the two jets are high, which results in a region of very low pressure between the jets.The jets deflected towards each other.The deformation is found in all numerical results; and each of the models with different nozzle spacing and pressure ratio has its own specific features.Figure 8 shows the numerical results of the model with /  = 6 and  0 /  = 6.8.Meanwhile, the experimental results also indicate the presence of jet deformation. 1 show the effect of various jet spacing on jet interaction.Figure 9 shows the contour of mean pressure along downstream cross-sectional planes numerical results at  0 /  = 6.8.The numerical results show a subatmospheric pressure in the region between double nozzles, compared with that of their outside facing region.The negative pressure is related to the mutual entrainment between jets [24], and the subatmospheric pressure grows as strong as the jet spacing decreases.Therefore, the plume of each jet is shown to "bend" towards each other, because of the different pressure between mixed region and outward facing region of two jets.spacings.It is observed that the increased jets spacing shifts the merge point further downstream.The region from nozzle outlets (/  = 0) to the merge point is the merging region, which is characterized by reverse flow in this region.From merge point inner shear layers of the jets begin to merge and are characterized as velocity is zero.The merge point is also characterized by high pressure.The contour of mean velocity along downstream cross-sectional plane (on the plane  = 0) numerical results is presented in Figure 11, and the numerical results are consistent with its experimental results.The merge point locations and jets spacing are given in Table 2.We perform a regression analysis of the values shown in Table 2 to discover the relationship between merge point locations and jets spacing.Regardless of the pressure ratio effect, we can get the following expressions:

Effects of Jet Spacing. Tests 1∼8 in Table
The predictions based on (3) and ( 4) are presented in Figure 12.It can be observed that for numerical results and experimental results the relationship between the merge point and jet spacing is almost linear, so does the combine point.However, the slope of graph varies for merge point and combine point.

Effects of Pressure Ratio.
In order to investigate the effect of pressure ratio, we carry out the tests with pressure ratios 3.4 and 8.1 shown in Table 1.It is a moderate underexpanded jet since  0 /  is 3.4, which is less than 3.84, the criteria for a moderately underexpanded jet.Figures 12 and 13 are the contour of mean velocity along downstream cross-sectional planes (on the plane  = 0) numerical results at different pressure ratio.As pressure ratio increases, the effect of jet interaction decreases, and the merge (combine) point location moves downstream.Detailed measurements for merge point and combine point locations are explained in Tables 3  and 4. The merge point locations and jets spacing are given in Tables 3 and 4. Referring to Section 4.2, we can get the following expressions.
For pressure ratio 3.4, we have For pressure ratio 8.1, we have For the merge point, the relationship between the numerical results and the experimental results is given in Figures 14(a) and 15.It can be observed that for numerical results and experimental results the relationship between the merge point and jet spacing is almost linear.Meanwhile, the slope of graph varies with different pressure ratio, so does the combine point.
Figure 14(b) shows the location variation in combine point with different spacing.
We perform a regression analysis of the values shown in Tables 3 and 4 to discover the relationship between merge (combine) point locations, pressure ratio, and jets spacing.The following expressions can be obtained: The prediction errors based on ( 9) and ( 10) are presented in Tables 3 and 4. It can be observed that the equations based on pressure ratio and jets spacing improve the prediction accuracy.

Conclusions
The mixing phenomenon of the dual underexpanded jets systems has been studied.The critical characteristics of International Journal of Aerospace Engineering The two jets deflect towards inward facing region, and the deflection degree is determined by the jets spacing, pressure ratio, and turbulent intensity.Three typical regions (converging region, merging region, and combined region) are commonly reported.Along the downstream location, the two jets gradually resemble a self-similar signal jet.
The relationship between the merge point and jet spacing is almost linear; with different pressure ratio relationship is expressed by (3), (5), and (7).And (3), (5), and (7) would go as a criterion for design of various parallel jet systems such as cooling or boosting system.
The merge point location of two jet flows is affected by the jet spacing but also by the jet exit pressure ratio; and its relationship can be expressed by (9).And it is proved that the equation based on (9) can better its prediction accuracy.

Figure 4 :
Figure 4: The schematic diagram of computational domain.

Figure 5 :Figure 6 :
Figure 5: The computational mesh and zoom-in of nozzles.

Figure 8 :
Figure 8: Contour of mean velocity along downstream cross-sectional planes numerical results.
Figure 10 demonstrates the vectors of mean velocity at the downstream locations for eight different jet International Journal of Aerospace Engineering s/d e = 2 s/d e = 3 s/d e = 4 s/d e = 6 s/d e = 10 s/d e = 13 s/d e = 16 s/d e = 20

Figure 14 :
Figure 14: Variation in merge point and combine point for different spacing.

Figure 15 :
Figure 15: Variation in merge point and combine point for different spacing and pressure ratio.

Table 1 :
Conditions for PIV measurement.

Table 2 :
Predictions and errors of two points (merge point and combine point).

Table 3 :
Predictions and errors of two points (merge point and combine point) at  0 /  = 3.4.