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Comparison of three-dimensional density distribution of numerical and experimental analysis for twin jets

Abstract

Three-dimensional density fields of the twin jets were numerically and experimentally investigated. The present study focused on the comparison of the density distribution for the twin jets. The results obtained by the computational fluid dynamics (CFD) and three-dimensional background-oriented schlieren (3D-BOS) indicate that the periodic density fluctuation appears in the potential core each nozzle, and the flow structure of the twin jets is quite similar. The distribution of the normalized density value at the nozzle centerline agrees well with CFD and 3D-BOS. The density value of the shear layer between the nozzles increases as the interaction of the twin jets occurs. The trend of increasing and decreasing the interference between the nozzles was almost the same as each other. On the other hand, the position where the interaction of the twin jets starts and the growth rate of interaction were different. This is probably due to the effect of the laminar-to-turbulent transition occurred in the results of CFD. This result indicates that the laminar-to-turbulent transition can be estimated from the velocity fields obtained by CFD and particle image velocimetry (PIV).

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number JP20H00278, JP19KK0361, JP17H03473 and JP21J20744. We used JAXA Supercomputer System generation 2 (JSS2) for the CFD analysis.

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Correspondence to Chungil Lee.

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Appendix A: Uncertainty analysis of 3D-BOS

Appendix A: Uncertainty analysis of 3D-BOS

The 3D-BOS uncertainty analysis was investigated by verifying the repeatability of the 3D-BOS method using the matrix formulation. Ten three-dimensional density fields of the twin jets can be obtained because we captured the ten background images at each projection angle. Here, three-dimensional density fields of the twin jets for each case are a well-averaged density fields because the shutter speed is sufficiently long averaging time. Figure 16 shows the profile results of the averaged density value and the standard deviation of the measurement for the xy and yz slices. The block line of this figure presents the averaged density value, and the gray region corresponds to the standard deviation. These results show that the standard deviation of the symmetric line and the yz slice at \(s/D =\) 12 is larger than those of the nozzle centerline and the yz slice at \(s/D =\) 4.

These standard deviations are caused by the deviations in the displacements of the background. Figure 17 shows the averaged displacement of vertical direction (x axis) and horizontal direction (y axis) in the projection angle 90\(^\circ\). Figure 18 shows the profile results of the averaged displacement value and the standard deviation in each displacement direction of the nozzle centerline (\(y/D =\) 0.5\(\times\)s) and symmetric line (\(y/D =\) 0). These results indicate that the standard deviation in each displacement direction is large, and in particular, the standard deviation in symmetric line is the largest. This is because the displacements vary in each case in the region where interaction of the twin jets occurs. These results illustrate that the larger standard deviation is observed in the area where interference between the nozzles occurs. Although the standard deviation is larger because of the interaction of the twin jets, the value is still sufficiently small in the area. Therefore, the 3D-BOS method using the matrix formulation is considered to be reliable.

Fig. 16
figure16

Standard deviation of the xy and yz slices

Fig. 17
figure17

Mean displacement in the projection angle 90\(^\circ\)

Fig. 18
figure18

Standard deviation of displacement

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Lee, C., Ozawa, Y., Haga, T. et al. Comparison of three-dimensional density distribution of numerical and experimental analysis for twin jets. J Vis (2021). https://doi.org/10.1007/s12650-021-00765-z

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Keywords

  • Background-oriented schlieren
  • Computational fluid dynamics
  • Three-dimensional density field
  • Supersonic twin jets