**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30123

##### Desktop High-Speed Aerodynamics by Shallow Water Analogy in a Tin Box for Engineering Students

**Authors:**
Etsuo Morishita

**Abstract:**

In this paper, we show shallow water in a tin box as an analogous simulation tool for high-speed aerodynamics education and research. It is customary that we use a water tank to create shallow water flow. While a flow in a water tank is not necessarily uniform and is sometimes wavy, we can visualize a clear supercritical flow even when we move a body manually in stationary water in a simple shallow tin box. We can visualize a blunt shock wave around a moving circular cylinder together with a shock pattern around a diamond airfoil. Another interesting analogous experiment is a hydrodynamic shock tube with water and tea. We observe the contact surface clearly due to color difference of the two liquids those are invisible in the real gas dynamics experiment. We first revisit the similarities between high-speed aerodynamics and shallow water hydraulics. Several educational and research experiments are then introduced for engineering students. Shallow water experiments in a tin box simulate properly the high-speed flows.

**Keywords:**
Aerodynamics compressible flow,
gas dynamics,
hydraulics,
shock wave.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.2363312

**References:**

[1] A. H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. 1, 2, New York, John Wiley & Sons, 1953.

[2] H. W. Liepmann and A. Roshko, Elements of as Dynamics, New York, John Wiley & Sons, 1960.

[3] B. W. Imrie, Compressible Fluid Flow, London, Butterworths, 1973.

[4] S. Shreier, Compressible Flow, New York, John Wiley & Sons, 1982.

[5] M. Van Dyke, An Album of Fluid Motion, Stanford, CA, Parabolic Pr., 1982.

[6] J. D. Anderson, Jr., Fundamentals of Aerodynamics, New York, McGraw-Hills, 1991.

[7] M. A. Saad, Compressible Fluid Flow, Englewood Cliffs, Prentice-Hall, pp.337-348, 1993.

[8] M. H. Aksel and O. C. Erap, Gas Dynamics, Prentice-Hall, New York, 1994.

[9] J. D. Anderson, Jr., Modern Compressible Flow: With Historical Perspective, New York, McGraw Hills, 2004.

[10] W. J. Orlin, N. J. Lindner and J.G. Bitterly “ Application of the analogy between water flow with a free surface and two-dimensional compressible gas flow,” NACA Rep. No. 875, 1947, pp.311-328.

[11] J. E. Hatch, “The application of the hydraulic analogies to problems of two-dimensional compressible gas flow”, M. Sc. Dissertation, Georgia School of Technology, March 1949.

[12] Y. Tomita, “A study of high speed gas flow by hydraulic analogy: The 4th report, flow around an airfoil”, Bulletin of JSME vol.2, no.8, pp. 663-669, Nov 1959.

[13] V. Kumar, I. Ng, G. J. Sheard, K. Houriganand and A. Fouras, “Hydraulic analogy examination of under expanded jet shock cells using reference image topography,” 8th International Symposium on Particle Image Velocimetry - PIV09, Melbourne, Victoria, Australia, August 25-28, 2009.

[14] P. K. Stansby, A. Chegini and T. C. D. Barnes, “The initial stages of dam-break flow,” Journal of Fluid Mechanics, vol. 374, Nov.1998, pp. 407-424.

[15] T. Okada, T. Ishido and E. Morishita, “High-speed Aerodynamics and Shallow Water Theory (in Japanese),” Proceeding of JSME Kanto Branch Symposium, 2012(18), pp. 155-156, March 2012.

[16] E. Morishita, “Compressible pipe flow and water flow over a hump,” Proceedings of the World Congress on Engineering 2013 Vol III, WCE 2013, July 3 - 5, 2013, London, U.K., 2013, pp.1739-1742.

[17] Y. Shimizu, “Non-uniform flow in open channel”, Chapter 4, Lecture Note of Hydraulics (in Japanese), Hydraulic Research Laboratory, Hokkaido University, 2017.

[18] S. Awazu and K. Kimura, Hydraulics Worked Examples (in Japanese), Tokyo, Ohm, 1979, pp.255-256.

[19] I. H. Shames, Mechanics of Fluids, New York, McGraw-Hill, 1993, pp.739-745.

[20] I. A. Bedarev, A. V. Fedorov and V. M. Fomin, “Numerical analysis of the flow around a system of bodies behind the shock wave,” Combustion Explosion and Shock Waves, vol.48, no.4, July 2012, pp 446–454.

[21] J. Sinclair and X. Cuia, “A theoretical approximation of the shock standoff distance for supersonic flows around a circular cylinder,” Physics of Fluids, vol. 29, 2017, 026102-pp.1-13.