Skip to main content
Log in

A numerical visualization technique based on the hydraulic analogy

  • Regular Paper
  • Published:
Journal of Visualization Aims and scope Submit manuscript

Abstract

The principles of experimental visualization are widely used in developing numerical visualization techniques. Numerous techniques have been created by the simulation of experimental techniques, such as dye, smoke, surface oil, and optical techniques. In this research, a numerical visualization technique is proposed by the computational modeling of the visualization process of hydraulic analogy. First, the principle and implementation of the current technique are introduced and defined, respectively. Then, flow datasets of double Mach reflection and Rayleigh–Taylor instability are used for examining the display effects of the current technique. The effects of physical parameters and specific heat ratio on the current technique are investigated. In addition, the current technique is compared with six other techniques. The comparison indicates that the current technique not only can accurately display shock waves and slip lines, but also has an advantage in stereoscopically and cleanly visualizing vortices. Furthermore, the relationship between the current technique and numerical Schlieren and Shadowgraph is discussed. The current technique is further improved for the presentation of the information of colors and illumination. Finally, the limits of the current technique are highlighted.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Buchanan A, Macartney R, Thompson MC et al (2007) Hydraulic analogy study of supersonic rectangular-jet screech control with cylinders. AIAA J 45:1539–1545

    Article  Google Scholar 

  • Dauptain A, Cuenot BM, Gicquel LY (2010) Large eddy simulation of stable supersonic jet impinging on flat plate. AIAA J 48:2325–2338

    Article  Google Scholar 

  • De Leeuw WC, Pagendarm HG, Post FH et al (1995) Visual simulation of experimental oil-flow visualization by spot noise images from numerical flow simulation. In: Scateni R, van Wijk JJ, Zanarini P (eds) Visualization in scientific computing’95. Springer, Vienna, pp 135–148

    Chapter  Google Scholar 

  • Drebin R A, Carpenter L, Hanrahan P (1988) Volume rendering. In: ACM Siggraph computer graphics, vol 22, no 4. ACM, pp 65–74

  • Gvozdeva LG, Predvoditeleva OA, Fokeev VP (1968) Double Mach reflection of strong shock waves. Fluid Dyn+ 3:6–11

    Article  Google Scholar 

  • Hadjadj A, Kudryavtsev A (2005) Computation and flow visualization in high-speed aerodynamics. J Turbul 6:N16

    Article  Google Scholar 

  • Heller HH, Bliss DB (1975) Aerodynamically induced resonance in rectangular cavities—physical mechanisms and suppression concepts. No: AFFDL-TR-74-133

  • Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94

    Article  MathSciNet  MATH  Google Scholar 

  • Jobard B, Lefer W (1997) Creating evenly-spaced streamlines of arbitrary density. In: Lefer W, Grave M (eds) Visualization in scientific computing’97. Springer, Vienna, pp 43–55

    Chapter  Google Scholar 

  • Klein EJ (1965) Interaction of a shock wave and a wedge-an application of the hydraulic analogy. AIAA J 3:801–808

    Article  Google Scholar 

  • Laramee RS, Hauser H, Doleisch H et al (2004) The state of the art in flow visualization: dense and texture-based techniques. Comput Graph Forum 23(2):203–221

    Article  Google Scholar 

  • Li GS, Xavier T, Charles H (2008) Physically-based dye advection for flow visualization. Comput Graph Forum 27:727–734

    Article  Google Scholar 

  • Liu X, Zhang S, Zhang H et al (2015) A new class of central compact schemes with spectral-like resolution II: hybrid weighted nonlinear schemes. J Comput Phys 284:133–154

    Article  MathSciNet  MATH  Google Scholar 

  • Loh WHT (1959) Hydraulic analogy for two-dimensional and one-dimensional flows. J Aerosp Sci 26:389–391

    Article  MATH  Google Scholar 

  • Peng Z, Laramee RS (2008) Vector glyphs for surfaces: a fast and simple glyph placement algorithm for adaptive resolution meshes. In: Proceedings of vision, modeling, and visualization 2008, pp 61–70

  • Post FH, Van Walsum T (1993) Fluid flow visualization. In: Hagen H, Müller H, Nielson GM (eds) Focus on scientific visualization. Springer, Berlin, pp 1–40

    Google Scholar 

  • Quirk JJ (1998) AMRITA—a computational facility (for CFD modelling). In: VKI 29th CFD series, pp 23–27

  • Sadarjoen IA, Post FH (2000) Detection, quantification, and tracking of vortices using streamline geometry. Comput Graph UK 24:333–341

    Article  Google Scholar 

  • Schneider D, Wiebel A, Carr H et al (2008) Interactive comparison of scalar fields based on largest contours with applications to flow visualization. IEEE Trans Vis Comput Graph 14:1475–1482

    Article  Google Scholar 

  • Settles GS, Hargather MJ (2017) A review of recent developments in Schlieren and Shadowgraph techniques. Meas Sci Technol 28:042001

    Article  Google Scholar 

  • Shadden SC, Lekien F, Marsden JE (2005) Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212:271–304

    Article  MathSciNet  MATH  Google Scholar 

  • Shi J, Zhang YT, Shu CW (2003) Resolution of high order WENO schemes for complicated flow structures. J Comput Phys 186:690–696

    Article  MathSciNet  MATH  Google Scholar 

  • Tamura Y, Fujii K (1990) Visualization for computational fluid dynamics and the comparison with experiments. In: Flight simulation technologies conference and exhibit. No: AIAA-1990-3031

  • Tropea C, Yarin AL (2007) Springer handbook of experimental fluid mechanics. Springer, Berlin

    Book  Google Scholar 

  • Von Funck W, Weinkauf T, Theisel H et al (2008) Smoke surfaces: an interactive flow visualization technique inspired by real-world flow experiments. IEEE Trans Vis Comput Graph 14:1396–1403

    Article  Google Scholar 

  • Worthing AG (1912) On the deviation from Lambert’s cosine law of the emission from tungsten and carbon at glowing temperatures. Astrophys J 36:345

    Article  Google Scholar 

  • Yates LA (1993) Images constructed from computed flowfields. AIAA J 31:1877–1884

    Article  Google Scholar 

  • Zhang S, Jiang S, Zhang YT et al (2009) The mechanism of sound generation in the interaction between a shock wave and two counter-rotating vortices. Phys Fluids 21:076101

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This study was supported and funded by the State Key Laboratory of Aerodynamics of China (No. SKLA2017-3-4).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jinsheng Cai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, J., Cai, J., Yang, D. et al. A numerical visualization technique based on the hydraulic analogy. J Vis 22, 371–384 (2019). https://doi.org/10.1007/s12650-018-0539-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12650-018-0539-6

Keywords

Navigation