The "limiting line" in mixed subsonic and supersonic flow of compressible fluids

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It is well known that the vorticity for any fluid element is constant if the fluid is non-viscous and the change of state of the fluid is isentropic. When a solid body is placed in a uniform stream, the flow far ahead of the body is irrotational. Then if the flow is further assumed to be isentropic, the vorticity will be zero over the whole filed of flow. In other words, the flow is irrotational. For such flow over a solid body, it is shown by Theodorsen that the solid body experiences no resistance. If the fluid has a small ... continued below

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Tsien, Hsue-Shen January 1, 1944.

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  • Main Title: The "limiting line" in mixed subsonic and supersonic flow of compressible fluids
  • Series Title: NACA Technical Notes

Description

It is well known that the vorticity for any fluid element is constant if the fluid is non-viscous and the change of state of the fluid is isentropic. When a solid body is placed in a uniform stream, the flow far ahead of the body is irrotational. Then if the flow is further assumed to be isentropic, the vorticity will be zero over the whole filed of flow. In other words, the flow is irrotational. For such flow over a solid body, it is shown by Theodorsen that the solid body experiences no resistance. If the fluid has a small viscosity, its effect will be limited in the boundary layer over the solid body and the body will have a drag due to the skin friction. This type of essentially isentropic irrotational flow is generally observed for a streamlined body placed in a uniform stream, if the velocity of the stream is kept below the so-called "critical speed." At the critical speed or rather at a certain value of the ratio of the velocity of the undisturbed flow and the corresponding velocity of sound, shock waves appear. This phenomenon is called the "compressibility bubble." Along a shock wave, the change of state of the fluid is no longer isentropic, although still adiabatic. This results in an increase in entropy of the fluid and generally introduces vorticity in an originally irrotational flow. The increase in entropy of the fluid is, of course, the consequence of changing part of the mechanical energy into heat energy. In other words, the part of fluid affected by the shock wave has a reduced mechanical energy. Therefore, with the appearance of shock waves, the wake of the streamline body is very much widened, and the drag increases drastically. Furthermore, the accompanying change in the pressure distribution over the body changes the aerodynamic moment acting on it and in the case of an airfoil decreases the lift force. All these consequences of the breakdown of isentropic irrotational flow are generally undesirable in applied aerodynamics. Its occurrence should be delayed as much as possible by modifying the shape or contour of the body. However, such endeavor will be very much facilitated if the cause or the criterion for the breakdown can be found first.

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  • Accession or Local Control No: 93R14296
  • URL: http://hdl.handle.net/2060/19930085006 External Link
  • Report No.: NACA-TN-961
  • Center for AeroSpace Information Number: 19930085006
  • Archival Resource Key: ark:/67531/metadc56878

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National Advisory Committee for Aeronautics Collection

The National Advisory Committee for Aeronautics (NACA) was a U.S. federal agency founded on March 3, 1915 to undertake, promote, and institutionalize aeronautical research. On October 1, 1958 the agency was dissolved, and its assets and personnel transferred to the newly created National Aeronautics and Space Administration (NASA).

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Creation Date

  • January 1, 1944

Added to The UNT Digital Library

  • Nov. 17, 2011, 10:13 p.m.

Description Last Updated

  • April 10, 2018, 3:42 p.m.

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Tsien, Hsue-Shen. The "limiting line" in mixed subsonic and supersonic flow of compressible fluids, report, January 1, 1944; (digital.library.unt.edu/ark:/67531/metadc56878/: accessed September 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.